Question

The perimeter of two similar triangles are 72 cm and 56 cm respectively. If one side of the first triangle is 18 cm, then the corresponding side of the smaller triangle is:

• A. 14 cm
• B. 18 cm
• C. 16 cm
• D. 12 cm

Answer 1

The correct option is A

14 cm

Since two triangles ABC and DEF are similar and then their perimeters will be proportional to the corresponding sides of the two triangles.

$\frac{{\text{Perimeter}}_1}{{\text{Perimeter}}_2}=\frac{18}{x}$
Where x = corresponding side of smaller triangle
$\frac{72}{56}=\frac{18}{x}$
$x=\frac{18\times 56}{72}$ = 14 cm

Hence, the corresponding side of the smaller triangle = 14 cm