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;

`(PQ)/(SQ)=(PR)/(ST)`

Substituting the values, we get;

`(x+5+8)/(8)=(21)/(x-9)`

`(x+13)/(8)=(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=(-4 \pm √(16+1140))/(2)}`

`x=(-4 \pm √(1156))/(2)}`

`x=(-4 \pm 36)/(2)}`

`x=(-4+36)/(2)} \ or \ x=(-4-36)/(2)}`

`x=(32)/(2)} \ or \ x=(-40)/(2)}`

`x=16 \ or \ x=-20`

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

Hence, the value of x is 16.