Question

The hypotenuse of rigt angled triangle is 6cm more than twice its shortest side. if third side is 2cm less than the hypotenuse , find sides of this triangle

Answer 1

Here's, your complete ans

Answer 2

$\large{\underline{\bf{\pink{Answer:-}}}}$

✰The sides of triangle are 10cm,24cm and 24cm.

$\large{\underline{\bf{\blue{Explanation:-}}}}$

$\large{\underline{\bf{\green{Given:-}}}}$

✰ Hypotenuse of triangle is 6cm more then twice the shorter side.

✰ the third side is 2cm less then the hypotenuse.

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the third side.

$\huge{\underline{\bf{\red{Solution:-}}}}$

Let the shorter side of triangle be x cm.

Then, its hypotenuse =(2x + 6)cm.

And , it's third side = (2x + 6-2)cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=(2x + 4)cm.

By using Pythagoras theorem

(2x +6)² = x²+ (2x + 4)²

$:\implies\:4x^2+24x+36=5x^2+16x+16$

$:\implies\:x^2-8x-20$

$:\implies\:x^2-10x+2x-20$

$:\implies\:x(x- 10)+2(x -10)$

$:\implies\:(x-10)(x+2)$

$:\implies\:x- 10=0 \:or\:x+2=0$

$:\implies\:x= 10 \:or\:x= -2$

$:\implies\:x= 10$[the side of ∆ can't be negative]

So,

The shorter side of triangle = 10cm

Longer side of triangle = (2×10+6)cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 24cm

And the hypotenuse of triangle =(2×10+6)cm⠀

=26cm

Hence,

The sides of triangle = 10cm, 24cm and 26cm

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