Question : $\triangle \mathrm{MNO}$ is similar to $\triangle \mathrm{STU}$. Perimeters of $\triangle \mathrm{MNO}$ and $\triangle \mathrm{STU}$ are 80 cm and 200 cm respectively. If ON = 25 cm, then what is the length of TU?
Option 1: 59 cm
Option 2: 61 cm
Option 3: 62.5 cm
Option 4: 60.5 cm
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Correct Answer: 62.5 cm
Solution :
The perimeter of $\triangle$MNO = 80 cm
The perimeter of $\triangle$STU = 200 cm
$\triangle$MNO is similar to $\triangle$STU, if ON = 25 cm
$\frac{\text{Perimeter of $\triangle$MNO}}{\text{Perimeter of $\triangle$STU}} = \frac{\text{ON}}{\text{TU}}$
⇒ $\frac{80}{200} = \frac{25}{\text{TU}}$
⇒ TU = $25\times{\frac{200}{80}}$
$\therefore$ TU = 62.5 cm
Hence, the correct answer is 62.5 cm.
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