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

Answer:

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

⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• 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,

⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• According to the Pythagoras theorem:-

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

⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf 50 = (a)^2 + (a)^2$

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➪ $\sf 50 = a^2 + a^2$

⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf 50 = 2 a^2$

⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ $\sf a^2 = \dfrac{50}{2}$

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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.