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

Solution:

Given, perimeter of a triangle = 50 cm

One side of a triangle is 4 cm longer than the smaller side

The third sides is 6 cm less than twice the smaller side

We have to find the area of the triangle.

Let the smaller side = x cm

One side = x + 4 cm

Third side = 2x - 6 cm

Perimeter of triangle = sum of all the sides of triangle

50 = x + 4 + x + 2x - 6

50 = 4x - 2

4x = 50 + 2

4x = 52

x = 52/4

x = 13 cm

So, smaller side = 13 cm

One side = 13 + 4 = 17 cm

Third side = 13(2) - 6 = 26 - 6 = 20 cm

By Heron’s formula,

Area of triangle = √s(s - a)(s - b)(s - c)

Where s = semiperimeter

s = (a + b + c)/2

Here, a = 13 cm, b = 17 cm and c = 20 cm

So, s = (13 + 17 + 20)/2

= 50/2

s = 25 cm

Area = √25(25 - 13)(25 - 17)(25 - 20)

= √25(12)(8)(5)

= √5 × 5 × 4 × 3 × 4 × 2 × 5

= (5 × 4)√5 × 3 × 2

= 20√30 cm²

Therefore, the area of the triangle is 20√30 cm².

✦ Try This: The perimeter of a triangle is 60 cm. One side of a triangle is 7 cm longer than the smaller side and the third side is 4 cm less than thrice the smaller side. Find the area of the triangle.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12

NCERT Exemplar Class 9 Maths Exercise 12.4 Problem 2

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

Summary:

The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. The area of the triangle is 20√30 cm²

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