Question

What is the value of x? Enter your answer in the box.

Answer 1

The shapes are similar.
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Therefore,
$\frac{42}{(15 + 42)} = \frac{x}{10 + x}$

Simplify:
$\frac{42}{57} = \frac{x}{10 + x}$
Cross multiply:
42(10+x) = 57x
420 + 42x = 57x
420 = 57x - 42x
420 = 15x
x = (420÷15)
x = 28