Question

the perimeter of a triangle is 108 m. The difference of three sides of the triangle from half its perimeter is 16 m,18 m, and 8 m respectively. Find the area of the triangle.

Answer 1

QUESTION;

The perimeter of a triangle is 108m .

The difference of three sides of the triangle from half of it's perimeter is 16m, 18m, and 8m respectively. Find the area.

To find: the sides and then the area of the triangle.

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Let us find the Length of the sides first:

Perimeter of the triangle is 108 m

Therefore ,the half of the perimeter is$\frac{108}{2}$= 54 m

Hence we can say

the Length of the first side is 54- 16 = 38 m

the Length of the second side is 54- 18 = 36m

and the Length of the third side is 54- 8 = 46m

Now, let us find the area.

Here the height of the triangle is not given .

THEREFORE

Area of the triangle (by herons formula)

= √s (s-a) (s-b) (s-c)

S = semi perimeter = 54 m

Area = √ 54× (54-38) (54-36) (54-46)

= √ 54× 16×18×8

= √ 2×3×3×3×2×2×2×2×2×3×3×2×2×2

= 2×2×2×2×3×3√(2×3)

= 144 × √2×3 m²

ANSWER: 144× √2×3 m²

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Hence completed.....