Question

If the sum of two sides of a right angled triangle is 23 cm and it's hypotenuse is 17 cm, find the sides​

Answer 1

Answer:-

Given:-

Sum of the sides of a right angled triangle containing right angle = 17 cm.

⟶ Base + Height = 17 cm.

Area of the triangle = 30 cm².

We know that,

Area of a right angled triangle = 1/2 * base * height

So,

⟹ 30 = 1/2 * base * height

⟹ 30 × 2 = base * height

⟹ 60 cm² = base * height

We know,

In a right angled triangle;

(Base)² + (Height)² = (Hypotenuse)²

[ Pythagoras Theorem ]

Also,

• (a + b)² - 2ab = a² + b²

Hence,

(Base + Height)² - 2 * base * height = (Hypotenuse)²

Putting the respective values we get,

⟹ (17)² - 2(60) = (Hypotenuse)²

⟹ 289 - 120 = (Hypotenuse)²

⟹ 169 = (Hypotenuse)²

⟹ (13)² = (Hypotenuse)²

⟹ 13 cm = Hypotenuse

∴ The length of hypotenuse of the given right angled triangle is 13 cm.