Each of the equal sides of an isosceles triangle measures 2 cm more th

1.	Each of the equal sides of an isosceles triangle measures 2 cm more than its height, and the base of the triangle measures 12 cm. Find the area of the triangle.
Answer» Let h be the height, then Each of the equal sides of an isosceles triangle = (h + 2) cm and Base = 12 cm Area of a triangle = 1/2 × Base × Height = 1/2 x 12 x h ….(1) Area of isosceles triangle = 1/4 x b x √(4a² – b²) = 1/2 x 12 x √(4(h+2)² – 144) …(2) From (1) and (2), we get 1/2 x 12 x h = 1/2 x 12 x √(4(h+2)² – 144) 6h = 3√(4h2 + 16h + 16-144) 2h = √(4h² + 16h-128) 4h² = 4h² + 16h – 128 16h = 128 or h = 8 Height is 8 cm. Now, Area of a triangle = 1/2 × Base × Height = 1/2 × 12 cm × 8 cm = 1/2 × 96 cm² = 48 cm². Answer!!

Each of the equal sides of an isosceles triangle measures 2 cm more than its height, and the base of the triangle measures 12 cm. Find the area of the triangle.

Answer»

Let h be the height, then

Each of the equal sides of an isosceles triangle = (h + 2) cm and

Base = 12 cm

Area of a triangle = 1/2 × Base × Height

= 1/2 x 12 x h ….(1)

Area of isosceles triangle = 1/4 x b x √(4a² – b²)

= 1/2 x 12 x √(4(h+2)² – 144) …(2)

From (1) and (2), we get

1/2 x 12 x h = 1/2 x 12 x √(4(h+2)² – 144)

6h = 3√(4h2 + 16h + 16-144)

2h = √(4h² + 16h-128)

4h² = 4h² + 16h – 128

16h = 128

or h = 8

Height is 8 cm.

Now,

Area of a triangle = 1/2 × Base × Height

= 1/2 × 12 cm × 8 cm

= 1/2 × 96 cm²

= 48 cm². Answer!!