Question

The perimeter of a triangle is 510 feet and the sides are in the ratio of 11:16:24.Find the area of the triangle

Answer 1

Given, hope it helps!

Explanation:

Perimeter= 510 feet

Perimeter is the sum of sides so..

16x + 11x + 24x = 510

51x = 510

x = 510/51 = 10

(10*24), (10*11), (10*16)

So the sides are 160ft 110ft and 240ft

Area is equal to √s(s-a)(s-b)(s-c)

where s is the semiperimeter= 510/2 = 255

and a, b and c are the sides

area =

√ 255(255-240)(255-110)(255-160)

= √ 255*15*145*95

= √ 52,689,375

= 7258.74 feet ^2

Answer 2

A=7258.74472

Explanation:

Multiply the side ratios by x

Add them together to get the perimeter

11x+16x+24x = 510

51 x =510

x = 10

The sides are 110, 160 240

We have to use herons formula

A = sqrt( p (p-a) (p-b)(p-c)) where p is the perimeter/2 and a,b,c are the side lengths

A = sqrt( 510/2 (510/2-110) (510/2-160)(510/2-240))

A = sqrt( 255 (145) (95)(15))

A = sqrt(52689375)

A=7258.74472