If the difference between the lengths of sides of a right angled triangle is $3$ cm , if perimeter of the triangle is $36$ cm. Find the area of the triangle.

Open in App

Solution

$l - b = 3$ cm $\Rightarrow l = 3 + b$

Perimeter $= l + b + \sqrt{l^{2} + b^{2}} = 36$

$\Rightarrow \sqrt{l^{2} + b^{2}} = 36 - (l + b)$

$\Rightarrow l^{2} + b^{2} = 1296 + l^{2} + b^{2} - 72 l - 72 b + 2 l b$

$\Rightarrow 72 l + 72 b = 1296 + 2 l b$

$\Rightarrow 36 l + 36 b = 648 + l b$

$\Rightarrow 36 (3 + b) + 36 b = 648 + (b + 3) b$

$\Rightarrow 108 + 72 b = 648 + b^{2} + 3 b$

$\Rightarrow b^{2} - 69 b + 540 = 0$

$\Rightarrow b = 60, 9$

$l = 63, 12$

$\Rightarrow$ Perimeter $= 36$

$\Rightarrow l = 12, b = 9$

$\Rightarrow A = \frac{1}{2} l b = 54$ .

Suggest Corrections

Similar questions

2 c m

24 c m^{2};

14

120

^{2}

3

54 c m^{2}

Join BYJU'S Learning Program