Question

The two legs of a right angle triangle are equal and square of its hypotenuse is50cm.sq. find length of each leg?​

Answer 1

Given:-

The square of the hypotenuse of right triangle is 50cm

And two legs are equal

To find

The length of each leg

A.T.Q

By Pythagoras

$\boxed{\purple{\sf{Hypotenuse {}^{2}=Base{}^{2}+Perpendicular {}^{2}}}}$

Let the leg be x

Then

$\sf\implies 50=x{}^{2}+x{}^{2}\\ \\ \sf\implies 50=2x{}^{2}\\ \\ \sf\implies \cancel{\dfrac{50}{2}}=x{}^{2}\\ \\ \sf\implies 25= x{}^{2}\\ \\ \sf\implies \sqrt{25}=x\\ \\ \sf\implies x=5cm$

Each leg of triangle is 5cm

Answer 2

$</p><p>\tt{\huge{\pink{Hello!!! }}}$

METHOD 1 :

Let the length of the legs of the right angled isosceles triangle be a cm.

Formula Used :

$</p><p>\huge{\boxed{\boxed{\tt{\purple{{Base}^2 + {Perpendicular}^2 = {Hypotenuse}^2$

$</p><p>\tt{\blue{\therefore{=>2{a}^2 \: = 2500 }}}$

$</p><p>\tt{\green{\therefore{=>a = \root{1250} = 50\root{2}}}}</p><p>$

Hence, the lengtg of each leg is 50√2 cm.

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METHOD 2 :

$</p><p>\tt{\purple{The \: Entire \: Solution \: Is \: In \: The \: Attachment... }}$

$</p><p>\tt{\huge{\red{\boxed{\boxed{Hope\: This\:Helps!!! }}}}}$

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