Question

the difference between the sides of a right angle triangle is 4 cm if area of the triangle is 70 cm^2. find the perimeter​

Answer 1

Step-by-step explanation:

Let one side of the right triangle be x cm

Hence, other side =(x - 4) cm

$\fbox {x - (x - 4) = x - x + 4 = 4} \: \\ area \: of \: right \triangle \: = \frac{1}{2} \times x \times (x - 4) \\ \implies 70 = \frac{1}{2} ( {x}^{2} - 4x) \\ \implies 140 = {x}^{2} - 4x \: \\ \implies {x}^{2} - 4x - 14 = 0 \\ \implies {x}^{2} - 14x + 10x - 140 \: = 0\\ \implies x({x} - 14) + 10(x - 14) \: = 0 \\ \implies (x + 10) (x - 14) = 0 \\ \implies (x + 10) = 0 \: or \: (x - 14) = 0 \\ \implies \: x = - 10 \: or \: x = 14 \\ but \: x \: can \: not \: be \: - ve \\ hence \: x \neq - 10 \\ therefore \: x = 14 \\ \implies \: x - 4 = 10 \\ {hyp}^{2} = {14}^{2} + {10}^{2} = 196 + 100 \\ \: \: \: \: \: \: \: \: \: \: \: = 296 \\ hyp \: = \sqrt{296} = \sqrt{4 \times 74} = 2 \sqrt{74} \\ perimeter \: of \: right \triangle \: = 10 + 14 + 2 \sqrt{74} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =( 24 + 2 \sqrt{74} )cm$