Question

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


1500root3

1500

1000

None

​

Answer 1

Here is your answer

1500 root 3 .

Answer 2

$\huge \fbox{answer}$

$\huge \rightarrow1500 \ \sqrt{3 {m}^{2} }$

$\fbox {explanation} \downarrow$

$\rm \rightarrow let \: {1}^{st} side \: be \: 3x$

$\rm \rightarrow let \: {2}^{nd} side \: be \: 5x$

$\rm \rightarrow let \: {3}^{rd} \: side \: be \: 7x$

$\rm \rightarrow perimeter = 300$

$\fbox {therefore}$

$\rightarrow 3x + 5x + 7x = 300$

$\rightarrow 8x + 7x = 300$

$\rightarrow 15x = 300 \\ \rightarrow x = \frac{300}{15} \\ \rightarrow x = 20$

$\fbox{value \: of \: x = 20}$

$\rm \rightarrow {1}^{st} side = 3x = 3 \times 20 = 60 \\ \rm\rightarrow {2}^{nd} side = 5x = 5 \times 20 = 100 \\ \rm \rightarrow {3}^{rd} side = 7x = 7 \times 20 = 140$

$\fbox{now...using \: herons \: formula}$

$\rm s = \frac{60 + 100 + 140}{2} = \frac{300}{2} = 150m$

$\fbox{area}$

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

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

$\rm a = \sqrt{150 \times 90 \times 50 \times 10} = \\ \rm \sqrt{6750000}$

$1500 \sqrt{3 {m}^{2} }$