Mensuration Ques 8
Question
The area of a right angled triangle is 80 sq. cm. The ratio of the base and the height of the triangle is $4: 5$. Find the length of hypotenuse.
(1) $\sqrt{82} cm$
(2) $2 \sqrt{82} cm$
(3) $2 \sqrt{41} cm$
(4) $3 \sqrt{82} cm$
(5) None of these
Show Answer
Correct Answer: (2)
Solution: (2)
Base $=4 x $ cm.
Height $=5 x $ cm.
Area $=\frac{1}{2} \times$ base $\times$ height
$\Rightarrow 80=\frac{1}{2} \times 4 x \times 5 x$
$\Rightarrow 10 x^{2}=80$
$\Rightarrow x^{2}=\frac{80}{10}=8$
$\Rightarrow x=\sqrt{8}=2 \sqrt{2} cm$
$\therefore$ Hypotenuse $=\sqrt{\text { base }^{2}+\text { perpendicular }^{2}}$
$=\sqrt{(4 x)^{2}+(5 x)^{2}}$
$=\sqrt{(16+25) x^{2}}$
$=\sqrt{41} x=\sqrt{41} \times 2 \sqrt{2}$
$=2 \sqrt{82} cm$
BETA
