How to find if rectangles are similar - PSAT Math
Card 0 of 35
Note: figure NOT drawn to scale.
Refer to the above figure.
, 
, 
.
Give the area of 
.
.
Note: figure NOT drawn to scale.
Refer to the above figure.
Give the area of
.
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, so the sides are in proportion - that is,
Set
, 
, 
and solve for 
:
has area
Set
Note: Figure NOT drawn to scale.
Refer to the above figure.
and 
.
What percent of 
has been shaded brown ?
Note: Figure NOT drawn to scale.
Refer to the above figure.
What percent of
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and 
, so the similarity ratio of 
to 
is 10 to 7. The ratio of the areas is the square of this, or
or
Therefore, 
comprises 
of 
, and the remainder of the rectangle - the brown region - is 51% of 
.
or
Therefore,
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the perimeter of 
.
Note: Figure NOT drawn to scale.
In the above figure,
Give the perimeter of
Tap to see back →
We can use the Pythagorean Theorem to find 
:
The similarity ratio of 
to 
is
so 
multiplied by the length of a side of 
is the length of the corresponding side of 
. We can subsequently multiply the perimeter of the former by 
to get that of the latter:
We can use the Pythagorean Theorem to find
The similarity ratio of
so
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of .
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of
Tap to see back →
Corresponding sidelengths of similar polygons are in proportion, so
, so
We can use the Pythagorean Theorem to find :
The area of 
is
Corresponding sidelengths of similar polygons are in proportion, so
We can use the Pythagorean Theorem to find
The area of
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of Polygon 
.
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of Polygon
Tap to see back →
Polygon 
can be seen as a composite of right 
and 
, so we calculate the individual areas and add them.
The area of 
is half the product of legs 
and 
:
Now we find the area of 
. We can do this by first finding 
using the Pythagorean Theorem:
The similarity of to implies
so
The area of 
is the product of 
and 
:
Now add: 
, the correct response.
Polygon
The area of
Now we find the area of
The similarity of
so
The area of
Now add:
Note: figure NOT drawn to scale.
Refer to the above figure.
, , .
Give the area of .
.
Note: figure NOT drawn to scale.
Refer to the above figure.
Give the area of
.
Tap to see back →
, so the sides are in proportion - that is,
Set
, , and solve for :
has area
Set
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the perimeter of .
Note: Figure NOT drawn to scale.
In the above figure,
Give the perimeter of
Tap to see back →
We can use the Pythagorean Theorem to find :
The similarity ratio of to is
so multiplied by the length of a side of is the length of the corresponding side of . We can subsequently multiply the perimeter of the former by to get that of the latter:
We can use the Pythagorean Theorem to find
The similarity ratio of
so
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of .
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of
Tap to see back →
Corresponding sidelengths of similar polygons are in proportion, so
, so
We can use the Pythagorean Theorem to find :
The area of is
Corresponding sidelengths of similar polygons are in proportion, so
We can use the Pythagorean Theorem to find
The area of
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of Polygon .
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of Polygon
Tap to see back →
Polygon can be seen as a composite of right and , so we calculate the individual areas and add them.
The area of is half the product of legs and :
Now we find the area of . We can do this by first finding using the Pythagorean Theorem:
The similarity of to implies
so
The area of is the product of and :
Now add: , the correct response.
Polygon
The area of
Now we find the area of
The similarity of
so
The area of
Now add:
Note: Figure NOT drawn to scale.
Refer to the above figure.
and .
What percent of has been shaded brown ?
Note: Figure NOT drawn to scale.
Refer to the above figure.
What percent of
Tap to see back →
and , so the similarity ratio of to is 10 to 7. The ratio of the areas is the square of this, or
or
Therefore, comprises of , and the remainder of the rectangle - the brown region - is 51% of .
or
Therefore,
Note: figure NOT drawn to scale.
Refer to the above figure.
, , .
Give the area of .
.
Note: figure NOT drawn to scale.
Refer to the above figure.
Give the area of
.
Tap to see back →
, so the sides are in proportion - that is,
Set
, , and solve for :
has area
Set
Note: Figure NOT drawn to scale.
Refer to the above figure.
and .
What percent of has been shaded brown ?
Note: Figure NOT drawn to scale.
Refer to the above figure.
What percent of
Tap to see back →
and , so the similarity ratio of to is 10 to 7. The ratio of the areas is the square of this, or
or
Therefore, comprises of , and the remainder of the rectangle - the brown region - is 51% of .
or
Therefore,
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the perimeter of .
Note: Figure NOT drawn to scale.
In the above figure,
Give the perimeter of
Tap to see back →
We can use the Pythagorean Theorem to find :
The similarity ratio of to is
so multiplied by the length of a side of is the length of the corresponding side of . We can subsequently multiply the perimeter of the former by to get that of the latter:
We can use the Pythagorean Theorem to find
The similarity ratio of
so
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of .
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of
Tap to see back →
Corresponding sidelengths of similar polygons are in proportion, so
, so
We can use the Pythagorean Theorem to find :
The area of is
Corresponding sidelengths of similar polygons are in proportion, so
We can use the Pythagorean Theorem to find
The area of
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of Polygon .
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of Polygon
Tap to see back →
Polygon can be seen as a composite of right and , so we calculate the individual areas and add them.
The area of is half the product of legs and :
Now we find the area of . We can do this by first finding using the Pythagorean Theorem:
The similarity of to implies
so
The area of is the product of and :
Now add: , the correct response.
Polygon
The area of
Now we find the area of
The similarity of
so
The area of
Now add:
Note: figure NOT drawn to scale.
Refer to the above figure.
, , .
Give the area of .
.
Note: figure NOT drawn to scale.
Refer to the above figure.
Give the area of
.
Tap to see back →
, so the sides are in proportion - that is,
Set
, , and solve for :
has area
Set
Note: Figure NOT drawn to scale.
Refer to the above figure.
and .
What percent of has been shaded brown ?
Note: Figure NOT drawn to scale.
Refer to the above figure.
What percent of
Tap to see back →
and , so the similarity ratio of to is 10 to 7. The ratio of the areas is the square of this, or
or
Therefore, comprises of , and the remainder of the rectangle - the brown region - is 51% of .
or
Therefore,
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the perimeter of .
Note: Figure NOT drawn to scale.
In the above figure,
Give the perimeter of
Tap to see back →
We can use the Pythagorean Theorem to find :
The similarity ratio of to is
so multiplied by the length of a side of is the length of the corresponding side of . We can subsequently multiply the perimeter of the former by to get that of the latter:
We can use the Pythagorean Theorem to find
The similarity ratio of
so
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of .
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of
Tap to see back →
Corresponding sidelengths of similar polygons are in proportion, so
, so
We can use the Pythagorean Theorem to find :
The area of is
Corresponding sidelengths of similar polygons are in proportion, so
We can use the Pythagorean Theorem to find
The area of
Note: Figure NOT drawn to scale.
In the above figure,
.
.
Give the area of Polygon .
Note: Figure NOT drawn to scale.
In the above figure,
Give the area of Polygon
Tap to see back →
Polygon can be seen as a composite of right and , so we calculate the individual areas and add them.
The area of is half the product of legs and :
Now we find the area of . We can do this by first finding using the Pythagorean Theorem:
The similarity of to implies
so
The area of is the product of and :
Now add: , the correct response.
Polygon
The area of
Now we find the area of
The similarity of
so
The area of
Now add: