Question

Eleanor has a garden in the shape of a right isosceles triangle. Two sides of the triangle measure 10 feet long each. What is the length of the third side?

103‾√
feet
cross out

B)
15
feet
cross out

C)
102‾√
feet
cross out

D)
20
feet

Answer 1

Solution :-

given that, two equal sides of a right angled isosceles triangle are 10 cm each .

So,

→ Perpendicular height of given ∆ = 10 feet

→ Base of given ∆ = 10 feet

→ Third side of given ∆ = Hypotenuse .

then,

→ (Hypotenuse)² = (Perpendicular)² + (Base)² { By pythagoras theorem }

→ Hypotenuse = √[(Perpendicular)² + (Base)²]

therefore,

→ Third side = √[(10)² + (10)²]

→ Third side = √[100 + 100]

→ Third side = √(200)

→ Third side = √(2 * 100)

→ Third side = √(2 * 10²)

→ Third side = 10√2 feet (Ans.)

Hence, the length of the third side is equal to 10√2 feet .

Learn more :-

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