Question

The perimeter of a triangular field is 450m and its sides are in the ratio 13: 12: 5. Find the area of the triangle?

Answer 1

HERE IS THE PROCESS DEAR ☺

Let the sides of the triangle be 13x, 12x and 5x

so,

the perimeter of the triangle = sum of all sides

450m = 13x+12x+5x

450m = 30x

x = 450m/ 30

= 15m

so,

the sides of the triangle is

1. 13x =13×15m = 195m
2. 12x = 12×15m = 180 m
3. 5x. = 5×15m. = 75 m

so, semiperimeter =(s) =450/2 =225m

so, the area of triangle

=√225(225-195)(225-180)(225-75)

= √15×15 × 30 × 45 × 150

=√ 15 ×15 ×15 ×2 ×15×3×2×3×5×5

= 15×15×2×3×5

=6750m²ans.

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thankyou ❤

ＬＯＶＥＹＯＵＲＳＥＬＦ

Answer 2

Let the sides of triangle be 13x , 12x and 5x

Perimeter=450m

13x+12x +5x= 450

30x = 450m

x= 15 m

First side = 13x=13(15m)=195 m

Second side = 12x=12(15m)=180 m

Third side = 5x= 5×(15m) = 75 m

Therefore, the sides of triangle are 195m,180m and 75m

Let a= 195 m, b= 180m and c= 75m

Semi perimeter= 450m/2=225 m

Using Heroin Formula

$Area \: of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \: \: \: \: = \sqrt{225(225 - 195)(225 - 180)(225 - 75 } \\ \: \: \: \: = \: \: \: \sqrt{225 \times 30 \times 45 \times 150} \\ \: \: \: \: = \sqrt{ {5}^{2} \times {3}^{2} \times 3 \times 5 \times 2 \times {3}^{2} \times \times 5 \times 2 \times 3 \times {5}^{2} } \\ \: \: \: \: = \sqrt{5 ^{6} \times {3}^{6} \times {2}^{2} } \ \ \\ \: \: \: = {5}^{3} \times {3}^{3} \times 2 \\ \: \: \: \: = 6750$

Therefore, area of triangle is 6750 m²