Question

The sides of right triangle are in the ratio of 3:4:5 and its perimeter is 12 cm. find uts area

Answer 1

Let the sides as 3x, 4x and 5x,
Perimeter= 3x+4x+5x
12=12x
So, x=1
And the sides are 3,4 and 5
Now ar(right triangle)= 1/2ab where a and b are legs
=1/2*3*4
=6 cm^2
So, area is 6 cm^2

Answer 2

6 cm square

Explanation:

let the side of triangle

a=3x ,b=4x,c=5x

perimeter of triangle = 12 cm

a+b+c = perimeter

3x +4x+ 5x= 12

12x = 12

x= 12÷ 12

x= 1 cm

side of triangle a= 3× 1 =3 cm

b=4 cm , c= 5 cm

semi perimeter (s)= perimeter ÷2

= 12÷ 2 = 6cm

by using heron's formula

area of triangle = √ s(s-a) ( s-b) ( s -c)

=√ 6(6-3) (6-4) (6-5)

= √ 6 × 3 ×2 × 1

= √ 2 ×3 ×3× 2 ×1

= 2 × 3 = 6cm square

hence the area of triangle is 6 cm square