Question

The sides of a triangular park area in the ratio of 5:8:7 and it's perimeter is 400m.Find it's area​

Answer 1

Answer:

The sides of a the triangular plot are in the ratio 3:5:7. So, let the sides of the triangle be 3x, 5x and 7x.

Also it is given that the perimeter of the triangle is 300 m therefore,

3x+5x+7x=300

15x=300

x=20

Therefore, the sides of the triangle are 60,100 and 140.

Now using herons formula:

S=260+100+140=2300=150 m

Area of the triangle is:

A=s(s−a)(s−b)(s−c)=150(150−60)(150−100)(150−140)=150×90×50×10=6750000

=15003 m2

Hence, area of the triangular plot is 15003 m2.

Answer 2

$\bold \color{green}{ \fbox { \fbox \red{required \: answer:-}}}$

$\bold{ { \underline{ \underline{given : }}}}$

ratio of side of triangular park :- 5:8:7

perimeter of triangular park :- 400m

let sides of triangle are 5x , 8x and 7x

we know that..

sum of sides of ∆ = perimeter of ∆

$\implies5x + 8x + 7x = 400 \\ \implies20x = 400 \\ \implies x= \frac{400}{20} \\ \implies \: x = 20$

so sides of triangle are:-

• 5×20 = 100m
• 8×20 = 160m
• 7×20 = 140m

now find the area of triangle by heron's formula..

$\bold{area \: = \sqrt{s(s - a)(s - b)(s - c)}}$

where

$\bold{s = \frac{perimeter}{2} }$

so here..

$\bold{s = \frac{400}{2} }$

$\bold{ar \triangle = \sqrt{200(200 - 100)(200 - 160)(200 - 140)}}$

$\bold{ar \triangle = \sqrt{200 \times 100 \times 40 \times 60}}$

$\bold{ar \triangle = 100 \sqrt{20 \times 10 \times 4 \times 6 }} \\ \bold{ar \triangle = 1000 \sqrt{2 \times 4 \times 6} } \\ \bold{ar \triangle = 4000 \sqrt{3} }$

so, area of rectangular park is 4000√3m² or 6928.20m²(approximately)