Question

find the area of a triangle with two sides 24cm and 18cm and perimeter 72cm​

Answer 1

Answer:

We know that,

Perimeter of a triangle=a+b+c

Let a=24cm

b=18cm

c=x cm

a+b+c=72

24+18+x=72

42+x=72

x=30cm

By using heron's formula,

Area of triangle=27×8=216cm²

Answer 2

Given :

• The two sides of a triangle = 24 cm and 18 cm.
• Perimeter of the triangle = 72 cm.

To Find :

• Area of the triangle.

Solution :

For finding the area of the triangle, first we need to find the third side of the triangle

Using Formula : Perimeter of triangle = Sum of all sides

$\longrightarrow \sf{Perimeter_{(Triangle)} = (Side)_{1} + (Side)_{2} + (Side)_{3}}$

$\longrightarrow \sf{72 = 24 + 18 + (Side)_{3}}$

$\longrightarrow \sf{72 = 42 + (Side)_{3}}$

$\longrightarrow \sf{72 - 42 = (Side)_{3}}$

$\longrightarrow \sf{(Side)_{3} = 30}$

• With this we got the third side of the triangle = 30 cm.

Now, we have :

• $\sf{(Side)_{1} = 24 cm}$
• $\sf{(Side)_{2} = 18 cm}$
• $\sf{(Side)_{3} = 30 cm}$

For finding the area of the given triangle, we should have to use Heron's Formula as all the sides of the triangle are different.

Using Formula : $\underline{ \boxed{ \sqrt{ \sf{s(s - a)(s - b)(s - c)}}}}$

Let, (a = 24), (b = 18), (c = 30)

• and first we need to find the value of s.

$\longrightarrow \sf{s = \dfrac{a+b+c}{2}}$

$\longrightarrow \sf{s = \dfrac{24+18+30}{2}}$

$\longrightarrow \sf{s = \cancel{\dfrac{72}{2}}}$

$\longrightarrow \sf{s = 36}$

• Hence we got s = 36

Putting the values in the Formula : $\sqrt{\bf{s(s - a)(s - b)(s - c)}}$

$\longrightarrow \sf{\sqrt{36(36-24)(36-18)(36-30)}}$

$\longrightarrow \sf{\sqrt{36 \times 12 \times 18 \times 6)}}$

$\longrightarrow \sf{\sqrt{46,656}}$

$\longrightarrow \sf{\sqrt{46,656}}$

$\longrightarrow \sf{216}$cm²

• Hence the area of the triangle = 216 cm²