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ACT Math : How to find if hexagons are similar

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Example Question #1 : How To Find If Hexagons Are Similar

Two hexagons are similar. If they have the ratio of 4:5, and the side of the first hexagon is 16, what is the side of the second hexagon?

Possible Answers:

12.8

$8\sqrt3$

$8\sqrt5$

Correct answer:

$8\sqrt5$

Explanation:

This type of problem can be solved through using the formula:

$\frac{A_1}{A_2}=\frac{X_1^{2}}{X_2^{2}}$

If the ratio of the hexagons is 4:5, then A_1=4 and A_2=5 . denotes area. The side length of the first hexagon is 16.

Substituting in the numbers, the formula looks like:

$\frac{4}{5}=\frac{16^2}{X_2^2}$

This quickly begins a problem where the second area can be solved for by rearranging all the given information.

$(X_2)^2= 16^2\cdot \frac{5}{4}= 256 \cdot \frac{5}{4}$

(X_2)^2=320

$(X_2)^2= \sqrt{320}$

The radical can then by simplified with or without a calculator.

Without a calculator, the 320 can be factored out and simplified:

$X_2= \sqrt {{\color{Red} 16} \cdot {\color{Red} 4} \cdot 5}$

$X_2=8\sqrt{5}$

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Example Question #2 : How To Find If Hexagons Are Similar

The ratio between two similar hexagons is 4:x . The side length of the first hexagon is 12 and the second is 17. What must be?

Possible Answers:

5.67

12.21

7.24

8.00

6.00

Correct answer:

8.00

Explanation:

This kind of problem can be solved for by using the formula:

$\frac{A_1}{A_2}=\frac{X_1^2}{X_2^2}$

where the values are the similarity ratio and the values are the side lengths.

In this case, the problem provides A_1 , but not A_2 . A_2 is denoted as in the question.

There are four variables in this formula, and three of them are provided in the problem. This means that we can solve for A_2 () by substituting in all known values and rearranging the formula so it's in terms of A_2 .

$\frac{4}{A_2}=\frac{12^2}{17^2}$

$A_2=4 \cdot \frac{17^2}{12^2} = 4\cdot \frac{289}{144}$

$A_2={\color{Blue} 8.0}$

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ACT Math : How to find if hexagons are similar

Study concepts, example questions & explanations for ACT Math

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Example Question #1 : How To Find If Hexagons Are Similar

Example Question #2 : How To Find If Hexagons Are Similar

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