Question

The side of a rectangular plot is 3:5:7 and its perimeter is 300m. Find its area.​

Answer 1

Let the sides of a triangular plot is 3x , 5x and 7x

3x + 5x + 7x = 300 m

15x = 300

x = 300/15

x = 20

then the sides of triangular plot is

3x = (3 × 20) = 60

5x = (5 × 20) = 100

7x = (7 × 20) =140

area of triangle=

A=√s(s−a)(s−b)(s−c)

=√150(150−60)(150−100)(150−140)

=√150(150−60)(150−100)(150−140)

=√150(150−60)(150−100)(150−140)

=√150×90×50×10

=√6750000 =1500 √3 m^2

area of plot is 1500 √3 m^2

Answer 2

EXPLANATIONS:-

Given:

The side of rectangular plot is 3:5:7.

The Perimeter is 300m

To Find :

the are of rectangular plot

Solution:-

suppose that the sides in meters , are 3x, 5x and 7x.

Then, We know that

$3x + 5x + 7x = 300( \sf{perimeter \: of \: triangle}$

$\therefore \: 15x = 300 \\ \implies \: x = \cancel\frac{300}{15} \: \\ \: \: \: \: \: \: (x = 20)$

So, the sides of triangle are :

$\boxed {3 \times 20m = 60m }\\ \boxed{5 \times 20m = 100m} \\ \boxed{ 7 \times 20m \: = 140m}$

$\rm{we \: can \: find \: the \: area \: using \: heron's \: formula}$

$\sf{ we \: have} , \: \: \: \blue {s = \frac{60 + 100 + 140}{2}m} \\ \\ = \boxed {\blue {\rm{150m}}}$

$\sf{and \: area \: will \: be, \: } \\ \\ \sqrt{150(150 - 60) (150 - 100)(150 - 140)} \\ \\ = \sqrt{150 \times 90 \times 50 \times 10} \: \: {m}^{2} \\ \\ = 1500 \sqrt{3} \sf{ {m}^{2} }$