Question

of the side of a triangular plot is in ratio 3:5:7 with its perimeter 300cm find the area of triangular plot​

Answer 1

Let the sides of the triangle be 3x, 5x and 7x repsectively and since the perimeter is 300m

${\tt So, 3x + 5x + 7x=300 }\\{\tt 15x = 300}\\{\tt x= \cancel \frac{300\:²⁰}{15\:¹}}\\{\mathbb x=20m}$

${\color{lightpink}\sf so,length \:of \:one\: side=60m}\\{\color{lightpink}\sf length \:of \:second \:side=100m}\\{\color{lightpink}\sf and \:length \:of \:third\: side=140m}$

${\color{red}▬{\color{navy}▬▬{\color{purple}▬▬{\color{springgreen}▬▬{\color{grey}▬▬{\color{aqua}▬▬{\color{gold}▬▬{\color{red}▬}}}}}}}}$

now according to herons formula -

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

$= \sqrt{150 \times 90 \times 50 \times 10}$

$= \sqrt{30 \times5 \times 30\times3 \times 5\times10 \times10}$

$= \: \sqrt{30^2 \times 5^2 \times 10^2 \times3}$

$= 30 \times 5 \times 10 \times \sqrt{3}$

$\purple{\boxed{\bf = \sqrt[1500]{3}}}$

${\color{red}▬{\color{navy}▬▬{\color{purple}▬▬{\color{springgreen}▬▬{\color{grey}▬▬{\color{aqua}▬▬{\color{gold}▬▬{\color{red}▬}}}}}}}}$

${\color{brown}●{\color{pink}●{\color{gold}●{\color{red}{\tt Hope\: {\mathfrak{\color{greenyellow}it\: {\bf{\color{springgreen}helps{\color{Ivory}●{\color{lightpink}●{\color{Magenta}●}}}}}}}}}}}}$

${\color {aqua} {\underbrace{\color {lime} {\overbrace{\color {#DA70D6}@ {\color {red} {\bf S {\color {springgreen} N {\color {yellow} E {\color {#00ffff} H{\color {pink} A {\color {purple}S{\color {#a52a2a}H {\color {#A9a9a9} I{\color {gold}S{\color {orange}H }}}}}}}}}}}}}}}}$

Answer 2

Suppose that the sides, in metres, are 3x,5x and 7x.

Then,

3x+5x+7x = 300 {perimeter of the ∆}

$15x = 300$

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

$x = 20$

So, the sides of the traingle are :-

• 3×20m = 60m
• 5×20m =100m
• 7×20m =140m

USING HERONS FORMULAE

√s(s-a) (s-b) (s-c)

Area =

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

$\sqrt{150 \times 90 \times 50 \times 10}$

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