Question

If the sides of a triangle are in the ratio 8:4:5 and its perimeter is 72 cm, find the area
of the triangle.​

Answer 1

As given in the question

Sides of the triangle are in ratio 8:4:5

Let the sides be 8x cm, 4x cm and 5x cm.

Also given

perimeter of the triangle is 72 cm

We know

Perimeter of the triangle is the sum of the sides of triangle i.e. Sum of length of three sides = perimeter

or

(8x + 4x + 5x) cm = 72 cm

17x = 72

or

x = 72/17

Thus sides of triangle are 8(72/17), 4(72/17) and 5(72/17)

= 576/17, 288/17 and 360/17 cm respectively

Also perimeter = 72

s (semi perimeter) = 36

Using Heron's formula

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

Now

s= 36

s-a = 36 - (576/17) = (612-576)/17 = 36/17

Similarly

s-b = (612-288)/17 = 324/17

and s-c = (612-360)/17 = 252/17

Using the following values in Heron's formula

$\sqrt{36(\frac{36}{17} )(\frac{324}{17} )(\frac{252}{17} )}$

By solving

$\frac{36}{17} \sqrt{\frac{(324)(252)}{17}}$

Also 324 is square of 18

Area =

$\frac{(36)(18)}{17} \sqrt{252/17} \\or\\\frac{648}{17} \sqrt{14.82}$

Thus area is approximately equal to 146.7 cm^2

P.s. - Unique set of sides, may be there is an error in the question itself.

Nevertheless,

Same method will be used for such type of questions.