Question

If the length of the hypotenuse of an isosceles right-angled triangle is √32 cm then its perimeter will be
a. 40 +√2
b. 8+√32
c. 30
d. 24

Answer 1

Answer:

b is the correct answer

Answer 2

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.