Geometry Practice Test 6

Area ΔABC = 20 $\mathit{c}{\mathit{m}}^2$
Area ΔDEF = 45 $\mathit{c}{\mathit{m}}^2$
AB = 5 cm
DE = x cm
{∵ The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides,
or (ΔABC) = ${\left(\mathit{A}\mathit{B}\right)}^2$
or (ΔDEF) = ${\left(\mathit{D}\mathit{E}\right)}^2$
$\frac{20}{45}$ = ${\left(\frac{5}{\mathit{x}}\right)}^2$
$\frac{20}{45}$ = $\frac{25}{{\mathit{x}}^2}$
x = $\sqrt{\frac{25\times 45}{20}}$
= $\sqrt{\frac{5\times 5\times 3\times 3\times 5}{20}}$
= $\frac{15}{2}$
= 7.5 cm