The sides of a right angle triangle containing the right angle are 5x and (3 x - 1) cm.If the area of triangle be 60 CM square, calculate the length of the side of triangle.
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We know the sides which aren't the hypotenuse are 5x cm and (3x-1) cm, and area is 60 sq cm.
Area of triangle = 1/2×base×height
60=1/2×5x×(3x-1)
120=15x²-5x
15x²-5x-120=0
Divide by 5
3x²-x-24=0
3x²+9x-8x-24=0
3x(x+3)-8(x+3)=0
(x+3)(3x-8)=0
So x= -3 or x=8/3
Lengths cannot be negative, so x=8/3.
The sides are 5(8/3) cm and 3(8/3)-1.
The sides are 40/3 cm and 7 cm.
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