The area of a right angle triangle is 63 sq.cm. The length of the base of the triangle is 5 cm. more than the altitute of the triangle. Find the length of the altitute of the triangle.

let the length of the altitute be x cm.

therefore length of the base is ( x + 5) cm.

area of the right angled triangle is (1/2) * base * altitude = (1/2)(x)( x + 5 )

but given that area = 63

therefore

(1/2)(x)( x + 5 ) = 63

or x(x+5) = 126

or

x ² + 5x - 126 = 0

solving

x ² + 14x -9x - 126 = 0

x( x +14 ) - 9( x + 14 ) = 0

( x - 9 ) ( x + 14 ) = 0

x = 9 or x = -14

ignoring negative value for x

x = 9 cm

therefore length of the altitude = 9 cm.

other word problems with some explanation

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