Question

The sides of a triangle are in ratio 25:17:12 and its perimeter is 1080 cm. Find the area.

Answer 1

GIVEN:

Ratio of sides of traingle = 25:17:12

Perimeter of the triangle = 1080

TO FIND:

Area of the triangle

SOLUTION:

Let the common ratio of sides be x

Sides of angles be 25x, 17, and 12x

We know that,

Perimeter of a triangle = Sum of all sides

According to the question,

25x + 17x + 12x = 1080

==> 54x = 1080

==> x = 20

Sides of the triangle:

25x = 25(20) = 500cm

17x = 17(20) = 340cm

12x = 12(20) = 240cm

Semi - Perimeter = 1080/2 = 540

Now, let's find the area of triangle using heron's formula.

Heron's Formula:

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

a = 500cm, b = 340cm and c = 240cm

$= \sqrt{540(540 - 500)(540 - 340) (540 - 240)} \\ \\ = \sqrt{540(40)(200)(300)} \\ \\ = \sqrt{540(2400000) }$

$= \sqrt{1296000000} \\ \\ = 36000$

Therefore, the area of triangle is 36000cm².

Answer 2

Given :-

Sides of ∆ are in the ratio 25:17:12

To find

• Area of triangle

We know that !

$\bigstar{\boxed{\sf{Perimeter\:of \ triangle =sum\ of \ all \ sides} }}$

Let the side of triangle be n

Side become 25n 17n and 12n

$\longmapsto\sf 25n +17n+12n=1080\\ \\ \longmapsto\sf 54n=1080\\ \\ \longmapsto\sf n=\cancel{\dfrac{1080}{54}}\\ \\ \longmapsto\sf n=20$

Now the sides of triangle

$\sf 25 n= 25\times 20 = 500cm\\ \\ \sf 17n= 17\times 20 =340cm\\ \\ \sf 12n = 12\times 20= 240cm$

Then , find the Area of triangle by Herons Formula

$\boxed{\sf{Area=\sqrt{s(s-a)(s-b)(s-c)}}}$

• Where "s" is semi perimeter and a,b and c are sides of triangle

$\longmapsto\sf s=\dfrac{a+b+c}{2}\\ \\ \longmapsto\sf s =\dfrac{500+340+240}{2}\\ \\ \longmapsto\sf s=\cancel{\dfrac{1080}{2}}\\ \\ \longmapsto\sf s= 540$

Now the Area of ∆

$\dashrightarrow\sf Area=\sqrt{s(s-a)(s-b)(s-c)}\\ \\ \dashrightarrow\sf Area= \sqrt{540(540-500)(540-340)(540-240)}\\ \\ \dashrightarrow\sf Area= \sqrt{540\times 40\times 200\times 300}\\ \\ \dashrightarrow\sf Area =\sqrt{60\times 3\times 3\times 40\times 40\times 5\times 60\times 5}\\ \\ \dashrightarrow\sf Area= 60\times 3\times 40\times 5\\ \\ \dashrightarrow\sf Area =180\times 200\\ \\ \dashrightarrow\sf Area\ of \ triangle=36000cm^2$

$\bigstar{\boxed{\sf{Area\:of\ triangle=36000cm^2}}}$