Question

The sides of a triangular plot are in the ratio of
3:5:7 and its perimeter is 300m. Find its area.​

Answer 1

Answer:

X = 20

Step-by-step explanation:

3x +5x + 7x = 300

15x = 300

X= 20

3 * 20 = 60

5 * 20= 100

7* 20 = 140

Answer 2

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: question\::-}}}}}$

the sides of a triangular plot are in the ratio of 3:5:7 and it's perimeter is 300m find its area

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: given\::-}}}}}$

the sides of a triangular plot are in ratio 3:5:7 and it's perimeter is 300m

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: to \: find\::-}}}}}$

its area

$\large\underline{\underline \red{\bigstar{\textbf{\textsf{\: solution\::-}}}}}$

let the side be 3x,5x,7x

now given perimeter = 300m

$\sf⇝ semi - perimeter = \frac{perimeter}{2}$

$\sf⇝ semi \: perimeter = \frac{300}{2}$

$\sf⇝ semi \: perimeter = 150m$

now by taking the sides perimeter = 300m

$\sf⇝ a + b + c = 300$

$\sf⇝ 3x + 15x + 7x = 300$

$\sf⇝ 15x = 300$

$\sf⇝ x = \frac{300}{15}$

$\sf⇝ x = 20$

now,

a = 3x = 3 × 20 = 60m

b = 5x = 5 × 20 = 100m

c = 7x = 7 × 20 = 140m

now, by using area of triangle

$\sf⇝ \sqrt{s(s - a)(s - b)(s - c)}$

$\sf⇝ \sqrt{150(150 - 60)(150 - 100)(150 - 140}$

$\sf⇝ \sqrt{15 \times (3 \times 5) \times 5 \times (10)^{4} }$

$\sf⇝ \sqrt{15 \times (3 \times 5) \times 3 \times (10) ^{4} }$

$\sf⇝ \sqrt{(15)^{2} } \times 3 \times (10)^{4}$

$\sf⇝ \sqrt{15^{2} } \times \sqrt{3} \times (10) ^{4}$

$\sf⇝ (15) \times \sqrt{3} \times (10)^{2}$

$\sf⇝ (15) \times 3 \times (100)$

$\sf⇝ 1500 \sqrt{3}$

so therefore the area is 1500√3