YuetteGalashaw
32

# two similar triangles have areas of 18 and 32 find the ratio and their perimeters

$\displaystyle \frac{l_1}{l_1'}=\frac{l_2}{l_2'}=\frac{l_3}{l_3'}=\frac{3}{4}(see \ below \ why) \\ l_1=\frac{3l_1'}{4} \\ l_2=\frac{3l_2'}{4} \\ l_3=\frac{3l_3'}{4} \\ \frac{P_1}{P_2}=\frac{l_1+l_2+l_3}{l_1'+l_2'+l_3'}=\frac{3(l_1'+l_2'+l_3')}{4(l_1'+l_2'+l_3')}=\frac{3}{4} \\ \\ \\ \text{The similarity ratio of two triangles equals the square root of the ratio between their areas} \\ \sqrt{\frac{18}{32}}=\frac{\sqrt{18}}{\sqrt{32}}=\frac{3\sqrt2\sqrt{32}}{32}=\frac{3\cdot 8}{32}=\frac{3}{4}$