Question

The sides of a triangle are $10$ cm,$10$ cm and $12$ cm. If each of the two equal sides is increased in the ratio $5:4$ but the third side remains unchanged, in what ratio has its perimeter been increased?

• A. $5:32$
• B. $5:37$
• C. $37:32$
• D. $32:37$

Answer 1

Answer: (C)

$37:32$

Given, sides of the triangle $=10cm,10cm,12cm$

$\therefore$ perimeter of the given triangle $=10+10+12=32cm$

As the two equal sides each $10cm$ increased in the ratio $5:4$

So, the corresponding sides of the new triangle$=10\times \frac{5}{4}=12.5cm$

Hence the 3 sides of the new triangles are $12.5cm,12.5cm,12cm$.

Then the perimeter of the new triangle $=12.5+12.5+12=37cm$

$\therefore$The ratio in which the perimeter of the new triangle is increased

$=\frac{perimeterofthenewtriangle}{perimeterofgiventriangle}=\frac{37}{32}$

Hence the ratio $=37:32$