Question

the sides of a triangle are in the ratio of 4:5:5 and its perimeter is 168 M find the area of a triangle

Answer 1

Let the sides of a triangle be 4x,5x,5x
As we know,
Perimeter of a triangle=Sum of all sides
so,
4x+5x+5x=168m
14x=168m
x=168/14
x=12m
so,
sides of a triangle are:
4x=4×12=48m
5x=5×12=60m
5x=5×12=60m
As we know,
Area of triangle=√(s-a)(s-b)(s-c)
where s is the semi perimeter of a triangle and a,,b,c are the sides of a triangle.
semi perimeter of a triangle=168/2
=84m
=√(84-48)(84-60)(84-60)
=√36×24×24
=√20736
=144m

Answer 2

Step-by-step explanation:

Sides Of The triangle are In The ratio 4x , 5x , 5x

area of triangle = a + b + c / 2

4x + 5x + 5x = 168

14x = 168

x = 168 / 14

x = 12

4x = 12 * 4.= 48

5x = 12 *5 = 60

5x = 12 *5 = 60

using herons formula

√s( S -a) (S -b) (S -c)

√12 ( 12 -48) ( 12 - 60) (12 -60)

√12 * 36 * 48 * 48

√2*2 *3 2*2 *3*3 *2*2*2*2*3 *2*2*2*2*3

√2*2*2*2 *2*2*2*2*2*2 *2 *2*3 3*3*3*3*

make perfect square

64√9 cm²