SAT Math : How to find the length of the diagonal of a rectangle
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Example Question #201 : Plane Geometry
What is the length of the diagonal of a rectangle that is 3 feet long and 4 feet wide?
The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:
Therefore the diagonal of the rectangle is 5 feet.
Example Question #202 : Plane Geometry
The length and width of a rectangle are in the ratio of 3:4. If the rectangle has an area of 108 square centimeters, what is the length of the diagonal?
12 centimeters
18 centimeters
9 centimeters
15 centimeters
24 centimeters
15 centimeters
The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3x and 4x.
We also know the area, so we write an equation and solve for x:
(3x)(4x) = 12x2 = 108.
x2 = 9
x = 3
Now we can recalculate the length and the width:
length = 3x = 3(3) = 9 centimeters
width = 4x = 4(3) = 12 centimeters
Using the Pythagorean Theorem we can find the diagonal, c:
length2 + width2 = c2
92 + 122 = c2
81 + 144 = c2
225 = c2
c = 15 centimeters
Example Question #201 : Sat Mathematics
Find the length of the diagonal of a rectangle whose sides are 8 and 15.
To solve. simply use the Pythagorean Theorem where 
Thus,
Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle
The above figure depicts a cube, each edge of which has length 18. Give the length of the shortest path from Point A to Point B that lies completely along the surface of the cube.
The shortest path is along two of the surfaces of the prism. There are three possible choices - top and front, right and front, and rear and bottom - but as it turns out, since all faces are (congruent) squares, all three paths have the same length. One such path is shown below, with the relevant faces folded out:
The length of the path can be seen to be equal to that of the diagonal of a rectangle with length and width 18 and 36, so its length can be found by applying the Pythagorean Theorem. Substituting 18 and 36 for 
Applying the Product of Radicals Rule:
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