Question

Each of the sides of a triangle is 4 cm less than the sum of its other two sides. Area of triangle in cm2

Answer 1

Area of the triangle is 4√3 cm²

Step-by-step explanation:

Let the three sides of a triangle are a, b, c cm.

By the question, each side is 4 cm less than sum of other two sides.

a = b + c - 4  --------(1)

b = a + c - 4

a = b - c + 4 ------(2)

c = a + b - 4  ----------(3)

From equation (1) and equation (2)

b + c - 4 = b - c + 4

2c = 8 ⇒ c = 4

From equation (1) and  (3)

a = b + (a + b - 4) - 4

a = a + 2b - 8

2b = 8

b = 4

From equation (1),

a = 4 + 4 - 4 = 4

Now a = b = c = 4 cm.

We know area of an equilateral triangle is given by A = $\frac{\sqrt{3}}{4}a^{2}$

For the given triangle, area = $\frac{\sqrt{3}}{4}(4)^{2}$

                                             = $4\sqrt{3}$ cm²

Therefore, area of the triangle will be 4√3 cm²

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