An isosceles right triangle has area 8 cm2. The length of its hypotenu

1.	An isosceles right triangle has area 8 cm2. The length of its hypotenuse is(A) √32 cm(B) √16 cm(C) √48 cm(D) √24 cm
Answer» (A) √32 cm Explanation: Let height of triangle = h As the triangle is isosceles, Let base = height = h According to the question, Area of triangle = 8cm² ⇒ ½ × Base × Height = 8 ⇒ ½ × h × h = 8 ⇒ h² = 16 ⇒ h = 4cm Base = Height = 4cm Since the triangle is right angled, Hypotenuse² = Base² + Height² ⇒ Hypotenuse² = 4² + 4² ⇒ Hypotenuse² = 32 ⇒ Hypotenuse = √32 Hence, Options A is the correct answer.

An isosceles right triangle has area 8 cm2. The length of its hypotenuse is(A) √32 cm(B) √16 cm(C) √48 cm(D) √24 cm

Answer»

(A) √32 cm

Explanation:

Let height of triangle = h

As the triangle is isosceles,

Let base = height = h

According to the question,

Area of triangle = 8cm²

⇒ ½ × Base × Height = 8

⇒ ½ × h × h = 8

⇒ h² = 16

⇒ h = 4cm

Base = Height = 4cm

Since the triangle is right angled,

Hypotenuse² = Base² + Height²

⇒ Hypotenuse² = 4² + 4²

⇒ Hypotenuse² = 32

⇒ Hypotenuse = √32

Hence, Options A is the correct answer.