Unit 6 similar triangles homework 5

1) x = 12

2) x = 23.1

3) x = 19

4) x = 16

5) x = 8

6) x = 17

Step-by-step explanation:

Comparing the sides of each triangle, we have;

1) =

Cross multiply to get,

(32 + x) * 24 = 32 * 33

768 + 24x =1056

24x = 1056 - 768

24x = 288

x = 12

2) =

cross multiply to have;

34x = 14 (33 + x)

34x = 462 + 14x

20x = 462

x = 23.1

3) =

cross multiply to have;

36 * 30 = 20(x + 35)

1080 = 20x + 700

1080 - 700 = 20x

380 = 20x

x = 19

4) =

cross multiply to have;

42.5(2x - 5) = 22.5(3x + 3)

85x - 212.5 = 67.5x + 67.5

collect like terms

85x - 67.5x = 67.5 + 212.5

17.5x = 280

x = 16

5) =

cross multiply to have;

(2x + 8)(x + 7) = (2x + 4)(x + 10)

2 + 14x + 8x + 56 = 2 + 20x + 4x + 40

2 + 22x + 56 = 2 + 24x + 40

collect like terms to have;

22x - 24x = 40 - 56

-2x = -16

x = 8

6) =

cross multiply to have;

82(2x + 8) = 28(7x + 4)

164x + 656 = 196x + 112

164x - 196x = 112 - 656

-32x = -544

x = 17

answer: for each 3 girls there is 2 boys . 3: 2

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step-by-step explanation: