Question

2) A side of an isosceles right angled triangle is 8 cm. Find the length of its
hypotenuse.​

Answer 1

Answer:

Step-by-step explanation:

a) Given, area of an isosceles right triangle = 8 cm2

Area of an isosceles triangle = 1/2 (Base x Height)

⇒  8 = 1/2 (Base x Base)

[∴ base = height, as triangle is an isosceles triangle]

⇒ (Base)2 =16 ⇒  Base= 4 cm

In ΔABC, using Pythagoras theorem

AC2 = AB2 + BC2 = 42 + 42 = 16 + 16

⇒ AC2 = 32 ⇒  AC = √32 cm

[taking positive square root because length is always positive]

Hence, the length of its hypotenuse is √32 cm.

Answer 2

Answer:

Let height of triangle = h

As the triangle is isosceles,

Let base = height =h

According to the question, Area of triangle = 8cm ²

1/2 ×Base×Height=8

1/2 ×h×h=8

h² =16

⟹h=4cm

Base = Height = 4cm

Since the triangle is right angled,

Hypotenuse² =Base ² +Height ²

Hypotenuse ² =4 ²+4²

⟹Hypotenuse ² =32

⟹Hypotenuse= root of 32 = 6

$\sqrt{32}$