Question

The ratio of the length of sides of a triangular park of our village is 2:3:4; perimeter of park
is 216 meter
Let us write by calculating the area of the park.
(ii) Let us write by calculating how long is to be walked from opposite vertex of longest
side to that side straightly.​

Answer 1

Answer:

• Area of the park = 1673.128m²

• how long is to be walked from opposite vertex of longest side to that side straightly = 34.8568m

Step-by-step explanation:

Given:-

• Ratio of triangular park = 2:3:4

• Perimeter = 216m

To Find:-

• Area of the park = ?

• how long is to be walked from opposite vertex of longest side to that side straightly = ?

Procedure:-

Let's assume the sides of the triangular park be 2x , 3x , 4x as first side, second side, and third side respectively.

Now, we know perimeter as 216m

From the given information we can infer that:-

$\implies \sf 2x + 3x + 4x = 216$

$\implies \sf 9x = 216$

$\implies \sf x = \dfrac{216}{2}$

$\implies \sf x = 24m$

• First side = 2x = 2× 24 = 48m

• Second side = 3x = 3 × 24 = 72m

• Third side = 4x = 4 × 24 = 96m

Finding area of triangle using Heron's formula:-

$\implies \sf \sqrt{s(s-a)(s-b)(s-b)}$

Semi-perimeter= 216/2 = 108m

$\implies \sf \sqrt{108(108-48)(108-72)(108-96)}$

$\implies \sf \sqrt{48(60)(36)(12)}$

$\implies \sf \sqrt{27994360}$

$\sf Area \ of \ triangle = 1673.128cm^2$

Finding how long is to be walked from opposite vertex of longest side to that side straightly (Altitude/height of the triangular village):-

48<72<96

So, Longest side = 96m

$\sf Area \ of \ triangular \ park = \dfrac{1}{2} \times height \times base$

$\sf \implies Area \ of \ triangular \ park = \dfrac{1}{2} \times 96 \times h$

$\sf \implies 1673.128 = 48h$

$\sf \implies \dfrac{1673.128}{48} = h$

→ 34.8568m = height

So, 34.8568m is to be walked from opposite vertex of longest side to that side straightly (Altitude/height of the triangular village)