Question

A right - angled triangle is isosceles. if the of the hypotenuse is 50m, what is the length of equal sides ?​

Answer 1

Correct Question:-

A right angle triangle is isosceles. If the square of the hypotenuse is 50m², What is the length of equal sides?

Answer:-

$\red{\bigstar}$ Length of equal sides $\large\leadsto\boxed{\tt\purple{5 \: m}}$

• Given:-

• Length of Hypotenuse of right angle triangle = 50 m

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• To Find:-

• Length of equal sides of the right angle triangle.

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• Solution:-

Let the equal sides of the right angle triangle be 'a'.

★ Figure:-

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf a}\put(2.8,.3){\large\bf a}\put(4.2,2.5){\large\bf 50}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\end{picture}$

We know,

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• According to the Pythagoras theorem:-

$\pink{\bigstar}$ $\underline{\boxed{\bf\blue{(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2}}}$

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➪ $\sf 50 = (a)^2 + (a)^2$

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➪ $\sf 50 = a^2 + a^2$

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➪ $\sf 50 = 2 a^2$

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➪ $\sf a^2 = \dfrac{50}{2}$

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➪ $\sf a^2 = 25$

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➪ $\sf a = \sqrt{25}$

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★ $\large{\bf\green{5 \: m}}$

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Therefore, the length of the equal sides of the right angle triangle are 5 m.

Answer 2

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Given:-

• Length of the hypotenuse right αngled isosceles triαngle = $\sf{50^2\:cm}$

To Find:-

• The length of the equαl sides.

Solution:-

Let the equαl side be x.

According to the Pythαgorαs theorem :-

$\large\boxed{\underline{\green{\sf (Hypotenuse ^2) =(perpendicular)^2+(Base)^2}}}$

Now,

$:\implies\:\: \sf{50^2=x^2+x^2}$

$:\implies\:\: \sf{50^2=2x^2}$

$:\implies\:\: \sf{x^2=\dfrac{50}{2} }$

$:\implies\:\: \sf{x^2=25 }$

$:\implies\:\: \sf{x=\sqrt{25} }$

$\sf:\implies \underline{\boxed{\pink{\mathfrak{x = 5\: m}}}}\bigstar$

∴ Length of the equαl sides of the right αngle triαngle αre 5 m.

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