Chapter Study Guide and Review 309

Similarity and Proportional Reasoning

29. Which quadrilateral is
    similar to quadrilateral
    ABCD?

(^34)
(^6165)
12
( )
' (^6) *
4
Find the value of x in each pair of similar
figures.

30. 40 m Y
    m

25 m 30 m

&'0 1

% ( /^2

31.

5 ft

# 12.5 ft $

" %

Y
ft

5 10.5 ft 6

4 7

EXAMPLE 7 Find the value of x in the

pair of similar figures.

#

"

21 ft $

24 ft

,

+

42 ft

Y
ft

_24 ft

42 ft

= _21 ft

x ft

Write a proportion.

24 · x = 42 · 21 Find the cross products.

24 x = 882 Multiply.

x = 36.75 Divide by 24.

The length of KL −− is 36.75 feet.

Perimeter and Area of Similar Figures (Lesson 3B)

32. DOLLHOUSES Franklin is building a
    dollhouse modeled after his house for his
    niece. He would like the scale factor to
    be _^1
    12
    . If the perimeter of his house is
    1,800 inches, what will be the perimeter
    of the dollhouse?


33. MEASUREMENT Two similar triangles have
    a scale factor of _^1
    5
    . Find the area of the
    larger triangle if the area of the smaller
    triangle is 6 square yards.

EXAMPLE 8 Cynthia is creating a poster

of a photograph she took. The photograph

is 5 inches by 7 inches. What will be the

area of the poster if the poster has

dimensions four times the photograph?

The scale factor relating the poster and the

photograph is 4.

area of

poster

= area of

photo

· (^) (4)^2
= (^) (5 · 7) · (^) (4)^2
= 560
The area of the poster is 560 in^2.
Lesson 3
" %

(^12) $

9
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