Question

in a right angle triangle the smaller side are(x+9)cm and (2x+3)cm find perimeter if its area is 54cm^2​

Answer 1

Area of right angled triangle = ½(length of perpendicular sides)

54 = ½(x+9)(2x+3)

108 = 2x²+3x+18x+27

2x²+21x-81=0

2x²-6x+27x-81 = 0

2x(x-3)+27(x-3) = 0

(x-3)(2x+27) = 0

Therefore, x=3 or -27/2

Substituting the values of x in the given sides we get their lengths as 12&9 or -4.5&-24. Since sides cannot be negative therefore x=3 hence the length of the sides are 12cm & 9cm.

Therefore, hypotenuse = √(144+81) =√(225) = 15cm.

Hence perimeter of the given triangle is 12+9+15 = 36cm.

Answer 2

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