Mensuration Ques 46
Question
The sides of a triangle are in the ratio $3: 4: 5$. Its area is 216 square $cm$. What will be the perimeter of this triangle?
(1) $72 cm$.
(2) $65 cm$.
(3) $70 cm$.
(4) $60 cm$.
(5) $68 cm$
(IBPS Bank PO MT CWE Prelim Exam, 04.12.2021)
Show Answer
Correct Answer: (1)
Solution: (1)
Let the sides of triangle be $3 x, 4 x$ and $5 x $ cm.
Here,
$(3 x)^{2}+(4 x)^{2}=9 x^{2}+16 x^{2}=$ $25 x^{2}=(5 x)^{2}$
$\therefore$ It is a right angled triangle.
Area of triangle $=\frac{1}{2} \times$ base $\times$ height
$\Rightarrow \frac{1}{2} \times 3 x \times 4 x=216$
$\Rightarrow x^{2}=\frac{216}{2 \times 3}=36$
$\Rightarrow x=\sqrt{36}=6$
$\therefore$ Perimeter of triangle $=3 x+4 x+5 x=12 x$
$=12 \times 6=72 cm$.
BETA
