The perimeter of an isosceles right triangle having area 100 cm^2 is

Q: The perimeter of an isosceles right triangle having area $100 cm^2$ is

(b) $20(\sqrt{2}+1) cm$ Let $a$ be the hypotenuse and $b$ be the length of each remaining side of the triangle. Then, $a^2=b^2+b^2 \Rightarrow a^2=2 b^2$ It is given that the area of the triangle is $100 cm^2$. $\therefore \quad \frac{1}{2} b \times b=100 \Rightarrow b^2=200 \Rightarrow b=10 \sqrt{2} cm$ Putting $b^2=200$ in $a^2=2 b^2$, we obtain $\begin{array}{ll}& a^2=400 \Rightarrow a=20 cm \\ \therefore \quad & \text { Perimeter }=a+2 b=(20+20 \sqrt{2}) cm=20(\sqrt{2}+1) cm\end{array}$

M.C.Q

CBSE - English Medium

The perimeter of an isosceles right triangle having area $100 cm^2$ is

A$20 \sqrt{2} cm$
B$20(\sqrt{2}+1) cm$
C
10 cm
D$(10+\sqrt{2}) cm$

STD 9
Maths
Herons Formula
RD Sharma

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