the sides of right angle triangle containing the rihht angle is 5x cm and 3x -1 ...

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August 2021 1 33 Report

the sides of right angle triangle containing the rihht angle is 5x cm and 3x -1 cm. if it's area is 60 cm², find its perimeter

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abhi569
$\boxed{\bold{ \: area \: of \: right \: angled \: triangle \: = \frac{1}{2} \times sides \: containing \: righ t \: angle}}$

So,

$60 = \frac{1}{2} \times 5x \times (3x - 1) \\ \\ \\ 60 \times 2 = 5x(3x - 1) \\ \\ \\ 120 = 15 {x}^{2} - 5x \\ \\ \\ 15 {x}^{2} - 5x - 120 = 0 \\ \\ \\ 3 {x}^{2} - x - 24 = 0 \\ \\ \\ 3 {x}^{2} - (9 - 8)x - 24 = 0 \\ \\ \\ 3 {x}^{2} - 9x + 8x - 24 = 0 \\ \\ \\ 3x(x - 3) + 8(x - 3) = 0 \\ \\ \\ (x - 3)(3x + 8) = 0 \\ \\ \\ x = 3 \: \: \: \: \: or \: \: \: \: \: x = - \frac{8}{3}$

Sides cant be -ve, taking +ve value,

So, sides are

5x = 5( 3 ) = 15 cm
3x - 1 = 3( 3 ) - 1 = 9 - 1 = 8 cm

By Pythagoras Theorem,

( 15 )^2 + ( 8 )^2 = hypotenuse^2

255 + 64 = Hypotenuse²

289 = Hypotenuse²

17 = hypotenuse

Hence,

Perimeter = Sum of all sides

Perimeter = 17 + 15 + 8

Perimeter = 40 cm

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