PSAT Math : How to find if rectangles are similar

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

Example Questions

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

Rectangles

Note: Figure NOT drawn to scale.

In the above figure,

.

.

Give the perimeter of .

Possible Answers:

Correct answer:

Explanation:

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:

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

Rectangles

Note: Figure NOT drawn to scale.

In the above figure,

.

.

Give the area of .

Possible Answers:

Insufficient information is given to determine the area.

Correct answer:

Explanation:

Corresponding sidelengths of similar polygons are in proportion, so

, so

We can use the Pythagorean Theorem to find :

The area of  is 

 

Example Question #323 : Plane Geometry

Rectangles

Note: Figure NOT drawn to scale.

In the above figure,

.

.

Give the area of Polygon .

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #3 : How To Find If Rectangles Are Similar

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above figure. 

 and .

What percent of  has been shaded brown ?

Possible Answers:

Insufficient information is given to answer the problem.

Correct answer:

Explanation:

 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 .

Example Question #4 : How To Find If Rectangles Are Similar

Rectangles

Note: figure NOT drawn to scale.

Refer to the above figure. 

.

Give the area of .

.

Possible Answers:

Correct answer:

Explanation:

, so the sides are in proportion - that is,

Set 

 and solve for :

 has area 

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: