Question

the perimeter of the triangle is 48m and it's sides are in the ratio of 13:12:5.Find the area of the triangle.​

Answer 1

$\boxed{\red{AnswEr:-}}$

A = 76.8 m^2

★ GivEn :-

The perimeter of the triangle is 48m.

It's sides are in the ratio of 13:12:5.

★ To Find :-

The area of the triangle.

★ Solution:-

The sides of the triangle are in the ratio of 13 : 12 : 5.

Let the common factor be x ( x > 0 )

Therefore,

The sides of the triangle are 13x m, 12x m, 5x m.

As per given,

$\sf{ 13x + 12x+5x=48}$

$\implies{\sf{ 30x=48}}$

$\implies{\sf{ x=\dfrac{8}{5}}}$

Now, the area of the triangle ( A ),

$\implies { \boxed{ \red{ \sf A = \dfrac{1}{2} \times b \times h}}}$

b = base and h = height

$\implies { \boxed{ \sf A = \dfrac{1}{2} \times 12 \times \dfrac{8}{5} \times 5 \times \dfrac{8}{5} }}$

$\implies { \boxed { \red{ \sf A =76.8 {m}^{2} }}}$

Answer 2

Solution

Given,

• the perimeter of the triangle is 48 m .
• its sides are in ratio 13:12:5

To find ,

• we have to find the area of the Triangle .

So,

let the ratio be in "x"

we know that

• angle A + Angle B + angle C = perimeter

not putting the value in the above equation we Get ;

=> 13x + 12x +5x = 48

=> 30x= 48

=> x = 48/30

=> x = 8/5 m

to find the area of the triangle we have to use the formula ;

1/2 X base X height

now substituting the value we get ;

=> 1/2 ×12×8/5×5×8/5

=> 76•8m^2

The area of the triangle is 76.8m square