Question

The perimeter of a triangle is 50cm. One side of the triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side. Find the area of the triangle.

Answer 1

Answer :

• Area of the triangle = 20√30 cm²

Given :

• The perimeter of a triangle is 50cm
• One side of the triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side

To find :

• Area of the triangle

Solution :

• Let the first smallest side be x

One side of the triangle is 4cm longer than the smaller side so,

• Let the second side be x + 4

Third side is 6cm less than twice the smaller side so,

• Let the third side be 2x - 6

Given , perimeter is 50cm so,

➟ x + (x + 4) + (2x - 6) = 50

➟ 4x = 52

➟ x = 52/4

➟ x = 13cm

• First side = x = 13cm
• Second side = x + 4 = 13 + 4 = 17cm
• Third side = 2x - 6 = 2(13) - 6 = 26 - 6 = 20cm

We know that Semi perimeter of triangle :

• s = a + b + c / 2

➟ 13 + 17 + 20 / 2

➟ 50/2

➟ 25cm

Finding the area of the triangle :

We know that :

• √s(s - a) (s - b) (s - c)

➟ √s(s - a) (s - b) (s - c)

➟ √25(25 - 13) (25 - 17) (25 - 20)

➟ √25 × 12 × 8 × 5

➟ 20√30 cm²

Hence , Area of the triangle = 20√30 cm²