Question

If bcd~gef find value of x

Answer 1

Answer:

$x = 13$

Step-by-step explanation:

Given

See attachment

Required

Find x

From the attachment, we have:

$BC = x + 4$

$BD = 2x - 7$

$GE = 51$

$GF = 57$

Because both triangles are similar, we use the following equivalent ratios:

$BC : BD = GE : GF$

Substitute values for each parameter

$x + 4 : 2x- 7 = 51 : 57$

Convert to fractions

$\frac{x + 4}{2x- 7} = \frac{51 }{ 57}$

Simplify the right-hand side

$\frac{x + 4}{2x- 7} = \frac{17}{19}$

Cross Multiply

$19(x + 4) = 17(2x - 7)$

$19x + 76 = 34x - 119$

Collect Like Terms

$19x - 34x = -76 - 119$

$-15x = -195$

Solve for x

$x = \frac{-195}{-15}$

$x = 13$