Question

if the ratio of the shortest and longest side of right angled triangle is 3 : 5 and it's perimeter = 36. finds its area

Answer 1

Answer:

Given that the ratio of the shortest and longest side of a right angled triangle

= 3: 5

let the constant ratio be ' x '

so now let the shortest side of right ∆

= 3 x

and the longest side of right ∆ = 5 x

since , the longest side of right ∆ = 5 x

so then , this side will be the hypotenuse of right ∆.

Find the third side of right ∆ :

let the third side be ' a '

a^2 = ( 5 x )^2 - ( 3 x )^2

a^2 = 25 x^2 - 9 x^2

a = √( 16x^2 ) = 4 x

perimeter of right ∆ = 36 cm

3 x + 4 x + 5 x = 36

12 x = 36 => x = 3

so now , sides are

3 x = 3 ×3 = 9 cm

4 x = 4 × 3 = 12 cm

5 x = 5 × 3 = 15 cm

therefore , area of right angled ∆

=( 1/ 2 ) × 9 × 12 = 54 cm^2

Your Answer : 54 cm^2

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