The perimeter of a right angled triangle is 72 cm and its area is 216 cm^2. The sum of the lengths of its perpendicular sides

Q: The perimeter of a right angled triangle is 72 cm and its area is $216 cm^2$. The sum of the lengths of its perpendicular sides is

(c) 42 cm Let the lengths of base and perpendicular be $a cm$ and $b cm$ respectively. Then, its hypotenuse is of length $\sqrt{a^2+b^2}$. It is given that the perimeter is 72 cm and area is $216 cm^2$. $\therefore \quad a+b+\sqrt{a^2+b^2}=72$$\quad$$\ldots$ (i) and, $\quad \frac{1}{2} a b=216 \Rightarrow a b=432$$\quad$$\ldots$ (ii) Now, $\quad a+b+\sqrt{a^2+b^2}=72$ $\Rightarrow(a+b)+\sqrt{(a+b)^2-2 a b}=72$ $\Rightarrow(a+b)+\sqrt{(a+b)^2-2 \times 432}=72$ $\Rightarrow x+\sqrt{x^2-864}=72$$\Rightarrow \sqrt{x^2-864}=(72-x)$ $\Rightarrow x^2-864=(72-x)^2$ $\Rightarrow x^2-864=72^2-144 x+x^2 \Rightarrow 144 x=5184+864 \Rightarrow 144 x=6048 \Rightarrow x=42$$\Rightarrow a+b=42 cm$.

M.C.Q

CBSE - English Medium

The perimeter of a right angled triangle is 72 cm and its area is $216 cm^2$. The sum of the lengths of its perpendicular sides is

A
36 cm
B
32 cm
C
42 cm
D
50 cm

STD 9
Maths
Herons Formula
RD Sharma

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