Question

the perimeter of a triangle is 30 cm whose two sides are 4cm and 5 cm find the area​

Answer 1

• No triangle is formed with sides 4 cm, 5 cm and perimeter as 30 cm.

Step-by-step explanation:

Given: We are given that perimeter of a triangle is 30 cm with sides 4 cm and 5 cm.

To find: We need to find the area of the triangle.

Solution:

Let us assume:

• First side = a = 4 cm
• Second side = b = 5 cm
• Third side = c = ?

We know that perimeter of a triangle is sum of all three sides of the triangle.

→ a+b+c = Perimeter

We know the values of a, b and perimeter. We are going to find the third side, which is c.

→ a+b+c = Perimeter

→ 4+5+c = 30

→ 9+c = 30

→ c = 30-9

→ c = 21 cm

Let us find the semi-perimeter of the triangle.

→ Semi perimeter = Perimeter/2

→ Semi perimeter = 30/2

→ Semi perimeter = 15 cm

Now, we are going to use Heron's formula to find the area of triangle. By applying the formula, we get:

→ Area = √s(s-a)(s-b)(s-c)

→ Area = √15(15-4)(15-5)(15-21)

→ Area = √15(11)(10)(-6)

→ Area = √15(11)(10)(-6)

→ Area = √-9900

We know that, the number inside the square root cannot be negative or less than 0. Hence, we can say that:

No triangle is formed with sides 4 cm, 5 cm and perimeter as 30 cm.