Question

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

Answer 1

Answer:

Solution:

a:b:c=3:5:7

a=3x=60

b=5x=100

c=7x=140

a+b+c=300

3x+5x+7x=300

15x=300

x=20

Semiperemeter=300/2=150

Herons formula

area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

=150(150−60)(150−100)(150−140)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

=15003–√m2

HOPE IT'S HELPFUL (•‿•)

Answer 2

☘️ Solution :

Let the sides be 3x, 5x and 7x.

We know that,

3x + 5x + 7x = 300 (perimeter of the triangle)

→ 15x = 300

→ x = 300/15

→ x = 20

Therefore, x = 20.

So, the sides of the triangle are :

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

Using Heron's formula :

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

So, now we have

$\sf \: s = \dfrac{60 + 100 + 140}{2} \: m = 150 m,$

$\begin{gathered}\implies \sf \: \sqrt{150(150 - 60) \: (150 - 100) \: (150 - 140) }\: m^{2} \\ \\ \implies \sf \: \sqrt{150×90×50×10}~m^{2}\\ \\ \implies \sf \purple{1500 \sqrt{3} m^{2}}\\ \\\end{gathered}$

☘️ Answer :

• 1500√3m^2