Question 130927
"In similar triangles, corresponding sides are proportional"

From the problem description, you can write:

{{{5x/5 = 4/x}}} "The ratio of the long side (5x) of the first triangle to the long side (5) of the second triangle is equal to the ratio of the base of the first triangle (4) to the base (x) of the second triangle".
Solve the above proportion for x.
{{{5x/5 = 4/x}}} Cross-multiply.
{{{5x^2 = 20}}} Divide both sides by 5.
{{{x^2 = 4}}} Take the square root of both sides (use only the positive answer).
{{{x = 2}}}
The lengths of the two unknown sides are:
{{{5x = 5(2)}}} = {{{10}}} and...
{{{x = 2}}}