Question

O c.
O d.
47. An isosceles right triangle has area 8 sq.cm. The lenghth of its
hypotenuse is​

Answer 1

✬ Hypotenuse = 4√2 cm ✬

Step-by-step explanation:

Given:

• Area of isosceles right angled triangle is 8 cm².

To Find:

• What is the length of hypotenuse ?

Solution: Let ABC be a isosceles right angled triangle. We know that in a isosceles triangle opposite sides and opposite angles are equal.

Here in ABC, we have

• AB = Perpendicular or height
• BC = Base
• AB = BC

Let assume that height = base = x.

★ Area of ∆ = 1/2(Base)(Height) ★

$\implies{\rm }$ 8 = 1/2(AB)(BC)

$\implies{\rm }$ 8 = 1/2(x)(x)

$\implies{\rm }$ 8 = x²/2

$\implies{\rm }$ 16 = x²

$\implies{\rm }$ √16 = x

$\implies{\rm }$ 4 cm = x

So, Meaure of perpendicular and base of isosceles triangle is of 4 cm.

[ Now by Pythagoras Theorem in ∆ABC ]

➭ AC² = AB² + BC²

➭ AC² = 4² + 4²

➭ AC² = 16 + 16

➭ AC² = 32

➭ AC = √32 = 4√2

Hence, the length of hypotenuse is 4√2 cm.

Answer 2

Hypotenuse = 4√2 cm.

Given :-

• Area of ΔABC = 8cm²
• AB = BC

To Find :-

• Length of AC (hypotenuse) = ?

Solution :-

Suppose AB = BC = " r " .

Area of ΔABC = 1/2 × Base × Height

=> 8 = 1/2 × BC × AB

=> 8 = r × r / 2

=> 8 × 2 = r²

=> 16 = r²

=> .°. r = 4cm.

Hence, AB = BC = 4cm.

In ΔABC , m∠ABC = 90°

=> AC² = AB² + BC² ----( According to Pythagoras theorem)

=> AC² = 4² + 4²

=> AC² = 32

=> AC = √32

=> AC = √4×4 × 2

=> AC = 4√2 cm.

Thus, the length of hypotenuse is 4√2cm.