Question

Find the sides of an isosceles right triangle of hypotenuse 5 root 2 cm

Answer 1

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Answer 2

Concept-

An isosceles triangle is a triangle which has two sides of equal length , sometime it is specified as having exactly two sides of equal length and sometime as having at least two sides of equal length of the isosceles right triangle.

Given-

ABC is an isosceles triangle whose sides are AB = BC

Find-

We need to find the sides of an isosceles right triangle of hypotenuse 5√2 cm.

Solution-

Given that,

Hypotenuse of the isosceles right triangle is 5√2 cm.

∴ Sides other than hypotenuse of  isosceles triangle are equal.

Let the other two sides be x each.

Using Pythagoras Theorem , we know that,

AB² + BC² = AC² → Equation (1)

i.e. , (perpendicular)² + (base)² = (hypotenuse)²

Putting values, AB = x = BC and AB = 5√2 cm in equation  (i), we get,

x² + x² = (5√2)²

[∴ √2 ×√2 = 2 , i.e. , (√2)² = 2]

2x² = 25 × 2

x² = 25

x = √25

x = 5 cm

Therefore, the required sides of an isosceles triangle are 5 cm each.

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