Unit 6 similar triangles homework 5

Answer:

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) [tex]\frac{32}{32 + x}[/tex] = [tex]\frac{24}{33}[/tex]

Cross multiply to get,

(32 + x) * 24 = 32 * 33

768 + 24x =1056

24x = 1056 - 768

24x = 288

x = 12

2) [tex]\frac{14}{34}[/tex] = [tex]\frac{x}{33 + x}[/tex]

cross multiply to have;

34x = 14 (33 + x)

34x = 462 + 14x

20x = 462

x = 23.1

3) [tex]\frac{20}{36}[/tex] = [tex]\frac{30}{x + 35}[/tex]

cross multiply to have;

36 * 30 = 20(x + 35)

1080 = 20x + 700

1080 - 700 = 20x

380 = 20x

x = 19

4) [tex]\frac{22.5}{42.5}[/tex] = [tex]\frac{2x - 5}{3x + 3}[/tex]

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) [tex]\frac{2x + 4}{2x + 8}[/tex] = [tex]\frac{x + 7}{x + 10}[/tex]

cross multiply to have;

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

2[tex]x^{2}[/tex] + 14x + 8x + 56 = 2[tex]x^{2}[/tex] + 20x + 4x + 40

2[tex]x^{2}[/tex] + 22x + 56 = 2[tex]x^{2}[/tex] + 24x + 40

collect like terms to have;

22x - 24x = 40 - 56

-2x = -16

x = 8

6) [tex]\frac{28}{82}[/tex] = [tex]\frac{2x + 8}{7x + 4}[/tex]

cross multiply to have;

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

164x + 656 = 196x + 112

164x - 196x = 112 - 656

-32x = -544

x = 17

The value of x in all the options can be determined by using the arithmetic operations. The calculations are given below.

1)

Given :

Two side lengths of a triangle are (x + 32) and 33.

According to the similar triangles property:

[tex]\dfrac{32+x}{32}=\dfrac{33}{24}[/tex]

SImplify the above expression in order to determine the value of 'x'.

768 + 24x = 1056

24x = 288

x = 12

2)

Given :

Two side lengths of a triangle are 34 and (x + 33).

According to the similar triangles property:

[tex]\dfrac{14}{34}=\dfrac{x}{33+x}[/tex]

SImplify the above expression in order to determine the value of 'x'.

34x = 462 + 14x

20x = 462

x = 23.1

3)

Given :

Two side lengths of a triangle are 36 and (x + 35).

According to the similar triangles property:

[tex]\dfrac{20}{36}=\dfrac{30}{35+x}[/tex]

SImplify the above expression in order to determine the value of 'x'.

1080 = 20x + 700

20x = 380

x = 19

4)

Given :

Two side lengths of a triangle are (3x + 3) and 42.5.

According to the similar triangles property:

[tex]\dfrac{22.5}{42.5}=\dfrac{2x-5}{3x+3}[/tex]

SImplify the above expression in order to determine the value of 'x'.

85x - 212.5 = 67.5x + 67.5

17.5x = 280

x = 16

5)

Given :

Two side lengths of a triangle are (2x + 8) and (x + 10).

According to the similar triangles property:

[tex]\dfrac{2x + 4}{2x+8}=\dfrac{x+7}{x+10}[/tex]

SImplify the above expression in order to determine the value of 'x'.

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

[tex]2x^2+22x+56=2x^2+24x+40[/tex]

16 = 2x

x = 8

6)

Given :

Two side lengths of a triangle are 82 and (7x + 4).

According to the similar triangles property:

[tex]\dfrac{28}{82}=\dfrac{2x+8}{7x+4}[/tex]

SImplify the above expression in order to determine the value of 'x'.

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

32x = 544

x = 17

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