7th Grade Math

300 Proportions and Similarity

Determine Perimeter

Two rectangles are similar. One has a length of 6 inches and a

perimeter of 24 inches. The other has a length of 7 inches. What

is the perimeter of this rectangle?

The scale factor is _^7

6

. The perimeter of the original is 24 inches.

x = (^24) ( ^7
6
(^) ) Multiply by the scale factor.
x = ^24241 (( _ 676 ))
4
1
Divide out common factors.
x = 28 Simplify.
So, the perimeter of the new rectangle is 28 inches.
a. Triangle LMN is similar -
1

. / 3 2

to triangle PQR. If the 24 m 18 m

perimeter of LMN is

64 meters, what is the

perimeter of PQR?

Determine Area

CONSTRUCTION The Eddingtons have

8 ft

5 ft

a 5-foot by 8-foot porch on the front

of their house. They are building a

similar porch on the back with double

the dimensions. Find the area of the

back porch.

The scale factor is 2.

The area of the front porch is (5)(8) or

40 square feet.

x = 40(2)^2 Multiply by the square of the scale factor.

x = 40(4) or 160 Evaluate the power.

The back porch will have an area of 160 square feet.

b. MURALS Malia is painting a mural on her bedroom wall. The

image she is reproducing is _ 201 of her wall and has an area of

36 square inches. Find the area of the mural.

Squaring Fractions

(^) ( (^201) ) 2 = 201 · 201
= 4001
Everyday Use
Perimeter A line or strip
protecting an area.
Math Use
Perimeter The distance
around the outside of a
closed figure.
293_303_C05_L3_895130.indd 300 12/29/09 1:10 PM