Question

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

Answer 1

Answer:

Step-by-step explanation:

ratio= 3:4:5

perimeter= 300 m

3x+4x+5x=300

12x = 300

x = 300÷12

x = 25m

Hope it helps you!!

Answer 2

Given :-

• The sides of a triangular plot are in the ratio:3:5:7
• It’s perimeter is 300m.

To Find :-

• Area of the triangle =?

Solution :-

Let the common ratio between the sides of the triangle be x.

• 1st side = 3x

• 2nd side = 5x

• 3rd side = 7x

As we know that:-

• The Perimeter of a triangle = Sum of sides of the triangle.

According to the question :-

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 3x + 5x + 7x = 300$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 15x = 300$

$\sf \: \: \: \: \: \: \: \: \: \:\:: \implies x = \dfrac{300}{15}$

$\sf \: \: \: \: \: \: \: \: \:\red{ \:\::\implies x = 20}$

Now let us find the measure of each side!

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 1st\: side \: (a) = 3x = 3 \times 20 = 60m$

$\sf \: \: \: \: \: \: \: \: \: \:\: :\implies 2nd \: side \: (b)= 5x = 5 \times 20 = 100m$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 3rd\: side \: (c) = 7x = 7 \times 20 = 140m$

$\sf \: \: \: \: \: \: \: \: \: \:\: :\implies Semi - perimeter \: (s) = \cancel{\dfrac{300}{2}} = 150$

According to the Heron's Formula:-

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

$\sf \: \: \: \: \: \: \: \: \: \:\:\leadsto\sqrt{150(150 - 60)(150 - 100)(150 - 140)}$

$\sf \: \: \: \: \: \: \: \: \: \:\:\leadsto\sqrt{150 \times 90 \times 50 \times 10}$

$\sf \: \: \: \: \: \: \: \: \: \:\: \leadsto\sqrt{6750000}$

$\sf \: \: \: \: \: \: \: \: \: \pink{\:\:\leadsto 1500\sqrt{3}}$

$\therefore\:\underline{\textsf{ Area of the triangle is \textbf{1500√3 m²}}}.$