Question

NEED HELP ASAP 80 POINTS

What is the value of x?



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x =

Answer 1

x = 7

Explanation:

The whole triangle and the small triangle are similar. Therefore the sides are in proportion.

We have the equation:

`((2x+10)+3)/(40+5)=(3)/(5)\\\\(2x+13)/(45)=(3)/(5)\qquad\text{cross multiply}\\\\5(2x+13)=(45)(3)\qquad\text{divide both sides by 5}\\\\2x+13=(9)(3)\\\\2x+13=27\qquad\text{subtract 13 from both sides}\\\\2x=14\qquad\text{divide both sides by 2}\\\\\boxed{x=7}`

Answer 2

x=7

Explanation:

We can use similar triangles and proportions to solve. Put the sides of the smaller triangle over the sides of the larger triangle.

5 3

----------- = -------------

40 +5 3 + (2x+10)

Simplify

5 3

----------- = -------------

45 (2x+13)

Cross multiply

5 *(2x+13) = 3*45

Divide by 5

5/5 *(2x+13) = 3*45/5

2x+13 = 3*9

2x+13 = 27

Subtract 13 from each side

2x+13-13 = 27-13

2x= 14

Divide by 2

2x/2 =14/2

x=7