the area of a right angled triangle is 600cmsq. if the base of the triangle exceeds the altitude by 10 cm , find the dimension of the triangle

Asked by eeshan.nk | 6th Aug, 2016, 03:59: PM

Expert Answer:

begin mathsize 12px style Let space the space altitudeof space the space rectangle space be space straight x space cm.
So comma space the space base space of space the space rectangle space equals space straight x plus 10 space cm
Area space of space the space rectangle space equals space 1 half cross times base space cross times space height space equals space 1 half cross times left parenthesis straight x right parenthesis space cross times left parenthesis straight x plus 10 right parenthesis equals fraction numerator straight x squared plus 10 straight x over denominator 2 end fraction
rightwards double arrow 600 equals fraction numerator straight x squared plus 10 straight x over denominator 2 end fraction
rightwards double arrow 1200 equals straight x squared plus 10 straight x
rightwards double arrow straight x squared plus 10 straight x minus 1200 equals 0
rightwards double arrow left parenthesis straight x plus 40 right parenthesis left parenthesis straight x minus 30 right parenthesis equals 0
rightwards double arrow straight x equals negative 40 space or space straight x equals 30
Since space altitude space cannot space be space negative comma space straight x equals 30 space cm
So comma space the space base space equals straight x plus 10 space cm equals 40 space cm
So comma space hypotenuse squared equals 30 squared plus 40 squared equals 900 plus 1600 equals 2500
rightwards double arrow hypotenuse equals 50 space cm
So comma space the space dimensions space of space the space triangle space are space 30 space cm comma space 40 space cm space and space 50 space cm. end style

Answered by Rebecca Fernandes | 6th Aug, 2016, 04:13: PM