Question

An isosceles right triangle has area 8cm²find the length of its hypotenuse
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Answer 1

Answer:

Both the perpendicular and base are equal in length.

So Area of triangle = 1/2 x b x h

Let b = h = y

1/2 x y x y = 8

y² = 16

y = 4

So Perpendicular = Base = 4 cm

Now by Pythagoras theorem,

4² + 4² = √ 16+ 16 = √32 = 4√2 cm

So required hypotenuse = 4√2 cm

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Answer 2

Step-by-step explanation:

We have an Isosceles Right angle Triangle

So the 2 sides of right angle Triangle are 8.

So we have:-

Base: 4cm

Height : 4m

Hypotenuse= 5.65 cm

For finding Hypotenise we need to use

Pythagoras Theorem:-

This theorem states that The sum of the square of base and the height of a right angle Triangle will give us the square of the hypotenuse of the same right angle Triangle.

So let us consider triangle ABC (Attachment)

We know that area of a Triangle is

1/2× Base× Height = 8cm²

x² = 16

x = 4 cm

AB²+ BC² = AC²

4²+4²= AC²

16+16= AC²

32 = AC²

AC= 4 root 2 or 5.65 cm.

Isosceles Right Angle Triangle

This is a right angle Triangle where height and base are of same length.

REMEMBER:-

Hypotenuse is the longest side of a right angle Triangle and is never equal to any of the sides of a right angle Triangle.