Question

For the pair of similar triangles . Find the value of x . The value of x is _(simplify your answer . Use a comma to separate answers as needed .)

Answer 1

Step 1 :

In this question, we are meant to find the value of x.

Using similar triangles,

`\begin{gathered} \frac{2x\text{ - 8}}{24}\text{ =}\frac{42}{x\text{ + 6}} \\ \end{gathered}`

Step 2 :

`\begin{gathered} (\text{ 2 x - 8 ) ( x + 6 ) = 24 x 42} \\ 2x^2\text{ + 12 x - 8 x - 48 = 1008} \\ 2x^2\text{ + 4 x - 48 = 1008} \\ 2x^2\text{ + 4x - 48 }-1008\text{ = 0} \\ 2x^2\text{ + 4 x- 1056 = 0} \end{gathered}`

Step 3 :

Solving the Quadratic Equation using the Quadratic Formulae:

`\begin{gathered} 2x^2\text{ + 4 x - 1056 = 0 , a = 2 , b }=\text{ 4, c = -1056} \\ U\sin g\text{ the Quadratic Formulae:} \\ x\text{ =}\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4 ac}}}{2a} \\ \\ x\text{ = }\frac{-\text{ 4 }\pm\text{ }\sqrt[]{(-4)^2\text{ - 4 ( 2 ) ( -1056 )}}}{2\text{ ( 2 )}} \\ \\ x\text{ = }\frac{-4\text{ }\pm\text{ }\sqrt[]{16\text{ + 8448}}}{4} \\ \\ x\text{ =}\frac{-4\text{ }\pm\text{ }\sqrt[]{8464}}{4} \\ \\ x\text{ = }\frac{-4\text{ }\pm\text{ 92}}{4} \\ \\ x\text{ =}\frac{-4\text{ + 92}}{4}\text{ or }\frac{-4\text{ -92}}{4} \\ \\ x\text{ = }(88)/(4)\text{ or }(-96)/(4) \\ \\ x\text{ = 22 or -24} \\ x\text{ = 22 (CO}\R RECT\text{ ) , x = -24 ( we ignore this value, since it is negative)} \\ x\text{ = 22} \end{gathered}`

CONCLUSION :

The value of x = 22.