Question

a right angle triangle is isosceles. if the square of the hypotenuse is 50m square, what is the length of each sides?

Answer 1

take triangle ABC where AC square = 50 m^2
angle B = 90
AB = BC
take AB = x

Pythagoras Thm.
AB^2+BC^2= AC^2
2x^2 = 50
x^2= 25
therefore x = 5
AB=BC=5

Answer 2

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}}⇝

5m

• 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}}}

(Hypotenuse)

2

=(Perpendicular)

2

+(Base)

2

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➪ \sf 50 = (a)^2 + (a)^250=(a)

2

+(a)

2

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➪ \sf 50 = a^2 + a^250=a

2

+a

2

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➪ \sf 50 = 2 a^250=2a

2

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➪ \sf a^2 = \dfrac{50}{2}a

2

=

2

50

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➪ \sf a^2 = 25a

2

=25

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➪ \sf a = \sqrt{25}a=

25

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★ \large{\bf\green{5 \: m}}5m

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