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Intermediate Geometry : Quadrilaterals

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Example Question #431 : Intermediate Geometry

A parallelogram has adjacent sides with the lengths of $\displaystyle 4$ and $\displaystyle 13$. Find a pair of possible adjacent side lengths for a similar parallelogram.

Possible Answers:

$\displaystyle 1$ and $\displaystyle 4$

$\displaystyle 12$ and $\displaystyle 26$

$\displaystyle 12$ and $\displaystyle 39$

$\displaystyle 1$ and $\displaystyle 3$

Correct answer:

$\displaystyle 12$ and $\displaystyle 39$

Explanation:

Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.

The ratio of the first parallelogram is:

4:13 $\displaystyle 4:13$

Applying this ratio we are able to find the lengths of a similar parallelogram.

$4:13=(4\times 3):(13\times3 )=12:39$ $\displaystyle 4:13=(4\times 3):(13\times3 )=12:39$

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

A parallelogram has adjacent sides with the lengths of $\displaystyle 15$ and $\displaystyle 5$. Find a pair of possible adjacent side lengths for a similar parallelogram.

Possible Answers:

1:4 $\displaystyle 1:4$

4:1 $\displaystyle 4:1$

1:3 $\displaystyle 1:3$

3:1 $\displaystyle 3:1$

Correct answer:

3:1 $\displaystyle 3:1$

Explanation:

Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.

The ratio of the first parallelogram is:

$15:5\rightarrow 3:1$ $\displaystyle 15:5\rightarrow 3:1$

Applying this ratio we are able to find the lengths of the second parallelogram.

$15:5=(15\div 5):(5\div 5)=3:1$ $\displaystyle 15:5=(15\div 5):(5\div 5)=3:1$

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

A parallelogram has adjacent sides with the lengths of $\displaystyle 28$ and $\displaystyle 8$. Find a pair of possible adjacent side lengths for a similar parallelogram.

Possible Answers:

4:1 $\displaystyle 4:1$

2:9 $\displaystyle 2:9$

7:2 $\displaystyle 7:2$

16:4 $\displaystyle 16:4$

Correct answer:

7:2 $\displaystyle 7:2$

Explanation:

Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.

The ratio of the first parallelogram is:

$28:8 \rightarrow 28\div4:8\div4 \rightarrow 7:2$ $\displaystyle 28:8 \rightarrow 28\div4:8\div4 \rightarrow 7:2$

Thus by simplifying the ratio we can see the lengths of the similar triangle.

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Intermediate Geometry : Quadrilaterals

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #431 : Intermediate Geometry

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

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

All Intermediate Geometry Resources

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