Question

Q21. The perimeter of a triangle is 48 cm and its base is 2 times of each equal side. Find
length of each side and area of triangle

Answer 1

Answer:

th equal side=12 cm

base= 24 cm

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Answer 2

Given :-

The perimeter of a triangle = 48 cm

Base of the triangle = 2 × Side

To Find :-

The length of each side.

The area of the triangle.

Solution :-

Let the equal sides of the triangle be x each.

Then, we know

Base = 2x

By the formula,

$\underline{\boxed{\sf Perimeter=a+b+c}}$

According to the question,

Perimeter = $\sf 2x+x+x=48$

$\sf 4x=48$

$\sf x=\dfrac{48}{4}$

$\sf x=12$

Base = $\sf 2 \times 12=24$

Hence, the sides of the triangle are 12 cm each.

Using Heron's formula,

$\underline{\boxed{\sf Area \ of \ a \ triangle=\sqrt{s(s-a)(s-b)(s-c)}}}$

Substituting their values,

Area = $\sf \sqrt{48(48-24)(48-12)(48-12)}$

Area = $\sf \sqrt{48 \times 24 \times 36 \times 36}$

Area = $\sf \sqrt{14929992 }$

Area = $\sf 1221.88 \ cm^{2}$

Therefore, area of the triangle is 1221.88 cm²