Question

The sides of traingular ploy are in the ratio 3:5:7 and its perimeter is 300 meter ,find its area

Answer 1

Question : -

The sides of a triangular plot are in the ratio of 3:5:7 and it's perimeter is 300 metre, find it's area.

Answer : -

Given that,

Ratio of sides = 3:5:7

Perimeter = 300 m

To find,

The area of the triangular plot = ?

Assumption : -

Let side a = 3x

Let side b = 5x

Let side c = 7x

Before finding the area, we have to find the length of each side.

Let x be the side.

Then our sides will be,

3x, 5x and 7x.

3x + 5x + 7x = 300 m [sum of all sides = perimeter]

15x = 300 m

x = $\frac{300\:m}{15}$

x = 20

[By substituting the value of x],

Side a = 3x = 3(20) = 60 m

Side b = 5x = 5(20) = 100 m

Side c = 7x = 7(20) = 140 m

Now, we've gotta the measurements of the sides and now we're abled to reckon area.

Area =

$\sqrt{s(s - a)(s - b)(s - c)}$

Where s = $\frac{a+b+c}{2}$

s = $\frac{60+100+140}{2}$

s = $\frac{300}{2}$

s = 150

You can also avoid this steps by directly dividing the perimeter by 2 as s stands for semi - perimeter.

Area =

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

Area =

$\sqrt{150(90)(50)(10)}$

Area =

$\sqrt{(2 \times 2 \times 3 \times 5)(2 \times 3 \times 3 \times 5)(2 \times 5 \times 5)(5 \times 2)}$

Area =

$2 \times 3 \times 5 \times 5 \times 2 \times 5 \sqrt{3}$

Area =

$1500 \sqrt{3}$

Area =

$1500 \times 1.73 \: (approximately)$

Area =

$2,595\:{cm}^{2}$