If the differcece between the sides of a right angled triangle is 3cm and its area is 54cm squre;find its perimeter.
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Let one side be x
Then another side will be x-3
Area of triangle = 1/2×base ×height
54 = 1/2× X × (X-3)
108 = X^2-3X
X^2 -3X - 108
X^2 - 12X +9X - 108
X(X-12) +9(X-12)
(X-12)(X+9)=0
X = 12 OR -9
But side of triangle cannot be negative therefore x = 12.
So base and height are 12 and 9.
Hypotenuse^2 = Base^2+ Height^2
Hypotenuse^2 = 144+81
Hypotenuse^2 = 225
Hypotenuse = 15
Perimeter of triangle = sum of all three side
= 15+12+9
= 36
Hope it helps.
Then another side will be x-3
Area of triangle = 1/2×base ×height
54 = 1/2× X × (X-3)
108 = X^2-3X
X^2 -3X - 108
X^2 - 12X +9X - 108
X(X-12) +9(X-12)
(X-12)(X+9)=0
X = 12 OR -9
But side of triangle cannot be negative therefore x = 12.
So base and height are 12 and 9.
Hypotenuse^2 = Base^2+ Height^2
Hypotenuse^2 = 144+81
Hypotenuse^2 = 225
Hypotenuse = 15
Perimeter of triangle = sum of all three side
= 15+12+9
= 36
Hope it helps.
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