Question

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

Answer 1

sides :- 3:5:7
let the sides be 3x, 5x and 7x
ATQ: 3x+5x+7x = 300
15x= 300
x= 300/15
x=20
side1:60
side2:100
side3:140

finding area by Heron's formula.....
$\sqrt{s \times (s - a)(s - b)(s - c)}$
finding s = 300/2
S=150
$\sqrt{150 \times(150-60)(150-100)(150-140)}$

$\sqrt{150 \times 90 \times 50 \times 10}${taking 150=50*3}

$50 \sqrt{90 \times 3\times 10}$

$50 \sqrt{9 \times 3\times 10 \times 10}$

$50 \times3\times10$*√3

$1500*√3$

area of given ∆ = 1500√3

Answer 2

$<i>Hi !$

Here is your answer !!

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

Perimeter = 300 cm

A.T.Q.

=> 3x + 5x + 7x = 300

=> 15x = 300

=> x = 300/15

=> x = 20 cm

3x = 3 × 20 = 60 cm

5x = 5 × 20 = 100 cm

7x = 7 × 20 = 140 cm

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To Find :

Area of the Triangle

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SOLUTION :

Semiperimeter ( s ) = 300/2 = 150 cm

$area \: = \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = > \sqrt{150 \: (150 - 60)(150 - 100)(150 - 140)} \\ \\ = > \: \sqrt{150 \times 90 \times 50 \times 10} \\ \\ = > \: \sqrt{3 \times 5 \times 10 \times 3 \times 3 \times 10 \times 5 \times 10 \times 10} \\ \\ = > \: 3 \times 5 \times 10 \sqrt{3} \\ \\ = > \: 150 \sqrt{3} {m}^{2} \: \: \: \: \: \: \: \: \: ans$

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Thanks !!