Question

The semi perimeter of a triangle is 132 cm and the product of the difference of its semi perimeter and its respective sides (in cm) is 13200 cm³ . Find the area of triangle

Answer 1

Answer:

The area of triangle is 1320 cm²

Step-by-step explanation:

Given :

• Semi perimeter of a triangle = 132cm

• Product of the difference of its semi perimeter and its respective sides = 13200 cm³

Find :

• The area of triangle

Solution :

Consider a Δ ABC with sides a, b and c

Let the semi-perimeter be s

Now, we are given that : 

s = 132 cm

Area of a triangle :

Therefore, according to the Heron's formula, 

★ Area of the triangle =

⇒ $\sqrt{s(s-a)(s-b)(s-c)}$

⇒ $\sqrt{132 \: \times \: 13200}$

⇒ $\sqrt{1742400}$

⇒ $1320 \: cm ^{2}$

Therefore,

The area of triangle is 1320 cm²

Answer 2

Appropriate Question:

• Two sides of a triangle are 5 cm and 7 cm and its semi-perimeter is 10 cm. Then the third side of the triangle is?

Given:

• Semi Perimeter of a triangle is 10 cm.
• Two sides of triangle are 5 cm and 7 cm respectively.

To find:

• The third side of the triangle.

Solution:

Let the third side of the triangle be c cm and other sides be a is 5 cm and b is 7 cm respectively.

As we know that,

★ Semi perimeter = Sum of all sides (a + b + c)/2

→ S = 5 + 7 + c/2

→ 10 = 12 + c/2

→ c = 20 - 12

→ = 8 cm ★

•°• Hence, the third side of the triangle is 8 cm.