Question

Please help!! Number 7

Answer 1

`x = 9`

Explanation:

Solving For #7

We will use the Angle Bisector Theorem

The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

In the figure provided in #7 we see that QS bisects ∠Q forming two smaller triangles ΔPQS and ΔQRS

According to the angle bisector theorem:

`(PQ)/(QR) = (PS)/(RS)\\\\\textrm{Or, alternatively}\\\\(QR)/(PQ) = (RS)/(PS)\\`

Given

`QR = 12.6\\PQ = 7\\RS = x\\PS = 5\\\\`

`(PQ)/(QR) = (PS)/(RS)\\\\\textrm{Or, alternatively}\\\\(QR)/(PQ) = (RS)/(PS)\\\\\\\rightarrow (12.6)/(7) = (x)/(5)`

If we multiply by
`5` both sides of the equation we can get rid of the denominator 5 on the right side:

`\rightarrow (12.6)/(7) * 5 = x\\\\9 = x\\\\\boxed{x = 9}`