Question

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

Answer 1

Step-by-step explanation:

$\huge {\boxed {\red{\boxed{\green {Answer }}}}}$

Let the sides of the triangle

be 3x, 4x and 5x.

_________________________

Given,

$\boxed{ Perimeter~ of~ Traingle~ =~ 300cm}$

_________________________

$\Large{\fcolorbox {red} {aqua} {Formula ~=~Sum~of~all~sides} }$

=> Perimeter of traingle = 3x + 4x + 5x

=> 3x +4x +5x = 300

=> 12x = 300

=> x = 300/12

=> x = 25

_________________________

Hence, the sides of triangle

are:-

=> 3x = 3 × 25

= 75 cm

=> 4x = 4 × 25

= 100cm

=> 5x = 5 × 25

= 125cm

_________________________

Proof :-

=> Perimeter = 300cm

=> 125 + 75 +100 = 300 cm

=> 300cm = 300 cm

_________________________

$\red {Hence, ~Sides~are~75cm, ~100cm~and~125cm}$

_________________________

Answer 2

$\huge {\underline {\underline \pink{ƛƝƧƜЄƦ}}}$

Given

• Ratio of sides = 3:5:7
• Perimeter = 300cm

To Calculate

• Area of Triangle

Solution

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

Sum of all sides = Perimeter

$\bf \implies 3x + 5x + 7x = 300$

$\bf \implies 15x = 300$

$\bf \implies x = 300 \div 15$

$\bf \implies x = 20cm$

Therefore, Sides of triangle are:-

• 3x = 3 × 20 = 60cm
• 5x = 5 × 20 = 100cm
• 7x = 7 × 20 = 140cm

Let a = 60cm, b = 100cm and c = 140cm

Semi Perimeter (s) = 300/2 = 150cm

Area of Triangle by Heron's Formula

$\bf\sqrt{s(s - a)(s - b)(s - c)}$

$\bf \sqrt{150(150 - 60)(150 - 100)(150 - 140)}$

$\bf \sqrt{150 \times 90 \times 50 \times 10}$

$\bf \sqrt{6750000}$

$\bf1500 \sqrt{3} {m}^{2}$