Question

The sides of a triangle
a triangle are in the ratio 5: 12: 14. If its perimeter is 90 cm,
find the area of the triangle.

Answer 1

Answer:-

In, place of 14 there must be 13 , because if we put the value 14....It will repeat

$Let \: first \: side \: be \: 5x \\ \: \: \: \: \: \: second \: side = 12x \\ \: \: \: \: \: \: third \: side = 13x$

Then,  

$Perieter \: of \: triangle = sum \: of \: all \: sides$

$5x + 12x + 13x = 90$

$30x = 90$

$x = 3$

Therefore, Sides are    

$5x = 5 \times 3 = 15cm \\ 12x = 12 \times 3 = 36cm\\ 13x = 13 \times 3 = 39cm$

Area

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

S =

$s = \frac{15+36+39}{2}$

$s = \frac{90}{2}$

S=45

$= \sqrt{45(45 - 15)(45 - 36)(45 - 39)}$

$= \sqrt{45 \times 30 \times 9 \times 6}$

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

$= 5 \times 2 \times 3 \times 3 \times 3$

$= {270cm}^{2}$

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