Question

Sides of a triangle are in the ratio 12;17:25 and its perimeter is 540cm. find its area...?
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Answer 1

$\huge \underline{ \mathbb{SOLUTION:-}}$

Given:

• Sides of a triangle are in the ratio of 12:17:25
• Perimeter of the triangle is 540cm

Need to find:

• Area of the triangle

Step by step explanation:

a = 12x

b = 17x

c = 25x

Perimeter = 540cm

a+b+c = 540

12x + 17x + 25x = 540

$\large \implies{54x = 540}$

$\large \implies{x = \frac{540}{54}} \\ \large \implies{x = 10}$

Therefore, sides are -

a = 10×12 = 120cm

b = 10×17 = 170cm

c= 25×10 = 250cm

Area of ∆$\small \implies{ \sqrt{s(s - a)(s - b)(s - c)}} \\ \small \implies{ \sqrt{270(270 - 120)(270 - 170)(270 - 250)}}$

$\small \implies{ \sqrt{270(150)(100)(20)}} \\ \small \implies{ \sqrt{81000000}} \\ \small \implies{\bold{9000 {cm}^{2} }}$