Question

The altitude of a triangle is 6 cm greater than its base. If its area is 108cm2 . Find its base and height

Answer 1

Answer:

LET , BASE = X

AND HEIGHT = X+6

SO, AREA OF TRIANGLE = 1/2*BASE*HEIGHT

       108 cm² = 1/2×(X+6)×(X)

===> 108×2 = X²+6X

==> 216 = X²+6X

==> X²+6X-216 = 0

==> A= 1 , B = 6 , C= -216

    D = B²-4AC

    ===> (6)²-4(1)(-216)

  ===> 36+864

   ==> 900

X= -B±√D / 2A

X = -6± √900/2(1)

X = -6±30/2

X = 2(-3±15)/2

X = -3±15

X = -3-15 AND -3+15

X = -18 AND 12

SO, BASE = 12

AND HEIGHT ==> 12+6 ==> 18

                            OR

==> X²+6X-216 = 0

      X²+18X-12X-216 = 0

     X(X+18)-12(X+18) = 0

 ==> (X+18) (X-12) = 0

==> X = -18, 12

SO, ANSWER NOT WILL BE NEGATIVE

SO, X = 12

SO, BASE = 12

HEIGHT = 6+12 ==> 18