Question

The perimeter of a triangular field is 450 m and its sides are in the ratio

13:17:15. Find the area of the triangle​

Answer 1

QUESTION:- The perimeter of a triangular field is 450 m and its sides are in the ratio

13:17:15. Find the area of the triangle.

ANSWER:-

$13.17.15 = 450 \\ \\ 13x + 17x + 15x = 450 \\ \\ 45x = 450 \\ \\ x = \frac{450}{45} \\ \\ x = 10 \\ \\ sides \: \: are \: \: \\ \\ 13(10) = 130 \\ \\ 17(10) = 170 \\ \\ 15(10) = 150$

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Answer 2

sides of a triangle in the ratio 13:

Let a,b,c

12:5

a:b:c = 13: 12:5 =>a=13x, b=12x, c=5x

.. Perimeter = 13x+12x+5x=450 => 30x=450

X = 15

..

a = 13x15=1957, b=12x15= 1804, C=5x15= 75m

Given that

2s = 450;

S = 225

Hence, area of triangle =

$\sqrt{ < s - a > < sbs - c}$

225(225-195)(225 – 180(225 –75)

=

$\sqrt{225 \times 30 \times 45 \times 150}$

$\sqrt{5 \times 3 \times 3 \times 5 \times 2 \times 3 \times 5 \times 5 \times 2 \times 3}$

$\sqrt{5 \times 3 \times 2}$

= 53 x 33 x 2 = 6750 m^2

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