Question

The sides of a triangular plot are in the ratio 2:3:4 and its perimeter is 900m. Its area is *

Answer 1

GIVEN :-

• Ratio of sides of ∆ are 2:3:4.
• Perimeter of ∆ = 900 m.

TO FIND :-

• Area of ∆.

SOLUTION :-

Let the ratio constant be "x".

.°. a = 2x , b = 3x , c = 4x.

• a , b and c are sides of ∆.

Now,

$\\ : \implies \displaystyle \sf \: Perimeter \: of \: \triangle = a + b + c$

$: \implies \displaystyle \sf \:900 = 2x + 3x + 4x$

$: \implies \displaystyle \sf \:900 = 9x$

$: \implies \displaystyle \sf \:x = \frac{900}{9}$

$: \implies \underline{ \boxed{ \displaystyle \sf \:x = 100}}$

Therefore sides of triangle becomes ,

• a = 2x = 200.
• b = 3x = 300.
• c = 4x = 400.

Now,

$\\ : \implies \displaystyle \sf \:semi \: perimeter \: of \: \triangle \: (s) = \dfrac{a + b + c}{2}$

$: \implies \displaystyle \sf semi \: perimeter \: of \: \triangle \: (s) =\frac{900}{2}$

$: \implies \underline{ \boxed{ \displaystyle \sf semi \: perimeter \: of \: \triangle \: (s) = 450 \: m.}}$

____________________

Now,

$\\ \dashrightarrow \displaystyle \sf \: Area \: of \: \triangle = \sqrt{s(s - a)(s - b)(s - c)}$

$\dashrightarrow \displaystyle \sf \:Area \: of \: \triangle = \sqrt{450(450 -200)(450 - 300)(450 - 400)}$

$\dashrightarrow \displaystyle \sf \:Area \: of \: \triangle = \sqrt{450 \times 250 \times 150 \times 50}$

$\dashrightarrow \displaystyle \sf \:Area \: of \: \triangle = \sqrt{843750000}$

$\dashrightarrow \underline{ \boxed{ \displaystyle \sf \:Area \: of \: \triangle = 29047.37 \: m ^{2} }}$

$\therefore \underline{\displaystyle \sf Area \ of \ triangle \ is \ 29047.37 \ m^{2}}$