Question

What is the value of x?



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Answer 1

The value of x is 7

Explanation:

In order to find this, we must create a proportion using the smaller triangle (right/left) and then the whole triangle (right/left)

5/3 = 45/2x+13

Now cross multiply to solve

5(2x + 13) = 45*3

10x + 65 = 135

10x =- 70

x = 7

Answer 2

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}`