Question

Each equal sides of an isosceles triangle is 2cm longer than its height.if the base of the triangle is 12cm.find the area of triangle

Answer 1

Answer :

• Area of the triangle = 48cm²

Given :

• Each equal sides of an isosceles triangle is 2cm more than its height
• The base of the triangle is 12cm

To find :

• Area of triangle

Solution :

To find the area of triangle we need to find the height of triangle by using the formula of area of triangle equal to area of isosceles triangle then we get answer of height of triangle after that we need to find the area of triangle

• Let the height of triangle be h

Given,

Each equal sides of an iscoscles triangle is 2cm more than its height so,

• a = h + 2

• Base of the triangle is 12cm

Now

• Area of the triangle = Area of the isosceles triangle

We know that

• Area of the triangle = 1/2 × b × h
• Area of the isosceles triangle = 1/4 × b√4a² - b²

➝ Area of the triangle = Area of the isosceles triangle

➝ 1/2 × b × h = 1/4 × b√4a² - b²

➝ 1/2 × 12 × h = 1/4 × 12√4(h + 2)² - (12)²

➝ 6h = 3√4h² + 16h + 16 - 144

➝ 2h = √4h² + 16h + 16 - 144

Now, squaring on both sides we get ,

➝ 4h² = 4h² + 16h + 16 - 144

➝ 16h - 128 = 0

➝ h = 128/16

➝ h = 8cm

Height of triangle = 8cm

Now Finding the area of the triangle :

• Area of the triangle = 1/2 × b × h

➝ 1/2 × 12 × 8

➝ 48cm²

Hence , Area of the triangle = 48cm²