How to find if quadrilaterals are similar

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ACT Math › How to find if quadrilaterals are similar

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1

The sides of rectangle A measure to , , , and . Rectangle B is similar to Rectangle A. The shorter sides of rectangle B measure each. How long are the longer sides of Rectangle B?

Explanation

In similar rectangles, the ratio of the sides must be equal.

To solve this question, the following equation must be set up:

$\small \frac{8}{12}=\frac{10}{x}$ , using $\small x$ as the variable for the missing side.

We then must cross multiply, which leaves us with:

$\small 8x=120$

Lastly, we divide both sides by 8 to solve for the missing side:

$\small \frac{8x}{8}=\frac{120}{8}$

Therefore, the longer sides of the rectangle are each .

2

Suppose a rectangle has side lengths of 7 and 3. Another rectangle has another set of side lengths that are 8 and 4. Are these similar rectangles, and why?

$\textup{No, they are not similar due to proportion.}$

$\textup{No, they are not similar due to length.}$

$\textup{No, they are not similar due to area.}$

$\textup{Yes, dimensions are only one unit more than the lengths of the other rectangle.}$

$\textup{There is not enough information.}$

Explanation

Set up the proportion to determine if the ratios of both rectangles are equal.

If they are, then they are similar.

$\frac{7}{3} =\frac{8}{4}?$

$\frac{7}{3} eq 2$

These are not similar rectangles since their ratios are not the same.

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