Question

If PQR ~ SQT, find the value of x

Answer 1

Given:

Given that the triangle PQR is similar to SQT.

The length of PS is (x + 5)

The length of SQ is 8.

The length of ST is (x - 9)

The length of PR is 21.

We need to determine the value of x.

Value of x:

Using the similar triangles property, we shall determine the value of x.

Hence, we have;

$\frac{PQ}{SQ}=\frac{PR}{ST}$

Substituting the values, we get;

$\frac{x+5+8}{8}=\frac{21}{x-9}$

 $\frac{x+13}{8}=\frac{21}{x-9}$

Cross multiplying, we get;

       $(x+13)(x-9)=(21)(8)$

$x^2+13x-9x-117=168$

         $x^2+4x-285=0$

The value of x can be determined using the quadratic formula.

Thus, we have;

$x=\frac{-4 \pm \sqrt{16+1140}}{2}}$

$x=\frac{-4 \pm \sqrt{1156}}{2}}$

$x=\frac{-4 \pm 36}{2}}$

$x=\frac{-4+36}{2}} \ or \ x=\frac{-4-36}{2}}$

$x=\frac{32}{2}} \ or \ x=\frac{-40}{2}}$

$x=16 \ or \ x=-20$

Since, x cannot take negative values, then x = 16.

Hence, the value of x is 16.