Question

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

Answer 1

Answer:

Area - 1500√3m.

Step-by-step explanation:

Consider the :

The sides of a triangular plot as -  3x , 5x and 7x.

Now,

⇒ 3x + 5x + 7x = 300 m

⇒ 15x = 300

⇒ x = $\sf\dfrac{300}{15}$

⇒ x = 20

The sides of triangular plot :

⇒ 3x = (3 × 20) = 60

⇒ 5x = (5 × 20) = 100

⇒ 7x = (7 × 20) = 140

Now,

The area of triangular plot :

$\sf\\ \implies \sqrt{s(s - a)(s - b)(s - c)}\\ \\\sf \implies \sqrt{150(150 - 60)(150 - 100)(150 - 140)}\\ \\ \sf \implies 1500 \sqrt{3\;{m}^{2} }$

Answer 2

AnswEr :

$\underline{\bigstar\:\textsf{According \: to \: given \: in \: question:}}$

$\:\bullet\:\sf\ Let \: the \: sides \: be \: 3x, 5x \: and \: 7x \: cm$

$\:\bullet\:\sf\ Perimeter = 300m$

$\:\bullet\:\sf\ Area =?$

$\rule{100}2$

$\normalsize\ : \implies{\boxed{\sf{Perimeter \: of \: triangle = Sum \: of \: all \: sides}}}$

$\normalsize\ : \implies\sf\ 300 = 3x + 5x + 7x \\ \\ \normalsize\ : \implies\sf\ 300 = 15x \\ \\ \normalsize\ : \implies\sf\ x = \frac{300}{15} = 20$

$\normalsize\ : \implies{\underline{\boxed{\sf \green{x = 20m}}}}$

$\rule{100}2$

$\:\star\:\sf\ First \: side(A) = 3x$

$\normalsize\ : \implies\sf\ A = 3x \\ \\ \normalsize\ : \implies\sf\ A = 3 \times\ 20 = 60$

$\normalsize\ : \implies{\underline{\boxed{\sf \orange{A = 60m}}}}$

$\:\star\:\sf\ Second \: side(B) = 5x$

$\normalsize\ : \implies\sf\ B = 5x \\ \\ \normalsize\ : \implies\sf\ B = 5 \times\ 20 = 100$

$\normalsize\ : \implies{\underline{\boxed{\sf \orange{B = 100m}}}}$

$\:\star\:\sf\ Third \: side(C) = 7x$

$\normalsize\ : \implies\sf\ C = 7x \\ \\ \normalsize\ : \implies\sf\ C = 7 \times\ 20 = 140$

$\normalsize\ : \implies{\underline{\boxed{\sf \orange{C = 140m}}}}$

$\rule{100}2$

$\normalsize\sf\ Now, \: Area \: of \: triangle;$

$\normalsize\ : \implies{\boxed{\sf{Area = \sqrt{s(s-a)(s-b)(s-c)} }}}$

$\normalsize\sf\ where;$

$\normalsize\ : \implies{\boxed{\sf{s = \frac{a + b + c}{2} }}}$

$\normalsize\ : \implies\sf\ s = \frac{60 + 100 + 140}{2} \\ \\ \normalsize\ : \implies\sf\ s = \frac{\cancel{300}}{\cancel{2}}$

$\normalsize\ : \implies{\underline{\boxed{\sf \blue{ s = 150m}}}}$

$\rule{100}2$

$\normalsize\ : \implies\sf\sqrt{s(s-a)(s-b)(s-c)} \\ \\ \normalsize\ : \implies\sf\sqrt{150(150-60)(150-100)(150-140)} \\ \\ \normalsize\ : \implies\sf\ \sqrt{150 \times\ 90 \times\ 50 \times\ 10} \\ \\ \normalsize\ : \implies\sf\ 1500\sqrt{3}$

$\normalsize\ : \implies{\underline{\boxed{\sf \blue{Area \: of \: triangle = 1500\sqrt{3} \: m^{2}}}}}$