Question

Please explain how to solve this problem.

Answer 1

Set up the proportion. That's what similar gives you the right to do.

(12 + 3)  / 4x = 12 / (3x + 1) Cross multiply
15 * (3x + 1) = 12 * 4x Remove the brackets
45x + 15 = 48x Subtract 45x from both sides.
15 = 48x - 45x
15 = 3x
x = 5

Answer 2

Answer:

The value of x is 5.

Step-by-step explanation:

It is given that both triangles are similar.

In triangle ABC and DEC,

$\angle ABC=\angle DEC$                           (Given)

$\angle ACB=\angle DCE=90^{\circ}$           (Given)

By AA rule of similarity,

$\triangle ABC\sim \triangle DEC$

The corresponding sides of similar triangles are proportional.

$\frac{AB}{DE}=\frac{BC}{EC}=\frac{AC}{DC}$

$\frac{4x}{3x+1}=\frac{3+12}{12}$

$12\times 4x=15\times (3x+1)$

$48x=45x+15$

$3x=15$

Divide both sides by 3.

$x=5$

Therefore the value of x is 5.