Question

If a triangle with side lengths as $5,12$, and $15$ cm is similar to a triangle which has longer side length as $24$ cm, then the perimeter of the other triangle is:

• A. $38.4$
• B. $44$
• C. $51.2$
• D. $58$

Answer 1

The correct option is C $51.2$

The longer side of the bigger triangle is $24$ cm.

The longer side of the smaller triangle is $15$ cm.

They are in ratio $24:15=\frac{24}{15}=1.6$

Thus, their perimeters also would be in the ratio $1.6$

The perimeter of the smaller triangle is $5+12+15=32$ cm

Implies the perimeter of the bigger triangle would be $32\times 1.6=51.2$ cm