Question

A triangle shaped land has the
sides in the ratio 3:5:7, if its perimeter is 300
meter. What will be the area of the land ? Ich
​

Answer 1

SOLUTION :-

Let the sides of the triangle shaped land be 3x, 5x and 7x.

Given that,

Perimeter of the triangle shaped land = 300 m

$\longrightarrow\sf 3x+5x+7x= 300\\\\\longrightarrow 15x= 300 \\\\\longrightarrow\bf x =20$

The sides of the triangle are 60m, 100m and 140m .

$\boxed{\bf Area \ of \ the \ triangle = \sqrt{s(s-a)(s-b)(s-c)} }$

Semi perimeter , s = 300/2 = 150 m

Area of the triangle = $\sf\sqrt{150(150-60)(150-100)(150-140}$

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

                                 = $\sf\sqrt{3\times5\times5\times2\times3\times3\times5\times2\times5\times5\times2\times5\times2}$

                                 = $\sf\sqrt{3^2\times 5^6\times 2^4\times 3}$

                                 = $\sf 3\times5\times5\times5\times2\times2\times\sqrt{3}$

                                 = $\bf 1500\sqrt{3} \ m$

                                   

Answer 2

AnswEr :-

• Area of the triangle is 1500√3m².

Given :-

• A triangle shaped land has sides in the ratio 3:5:7 and it's perimeter is 300m.

To Find :-

• Area of the triangle.

SoluTion :-

Put x in the ratio

Then, sides will be

• 3x
• 5x
• 7x

Formula for finding the perimeter of the triangle is :-

• Sum of all sides

According to question :-

3x + 5x + 7x = 300

→ 8x + 7x = 300

→ 15x = 300

→ x = 300/15

→ x = 20

Sides of the triangle are

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

Semi - perimeter (s) = 300/2 = 150

Area of the triangle is :-

√ s (s - a) (s - b) (s - c)

→ √ 150 (150 - 60) (150 - 100) (150 - 140)

→ √ 150 × 90 × 50 × 10

→ 1500√3m

Hence, the area of the triangle is 1500√3m².

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