The base of a triangle is twelve more than twice its height. if the area of the triangle is 51 square centimeters, find its base and height.

The base and height of the triangle whose area is 51 and base of a triangle is twelve more than twice its height are 21.49 cm and 4.745 cm respectively.

Solution:

Given that  

The base of a triangle is twelve more than twice its height

And area of triangle = 51 square centimeter  

Let’s assume height of triangle = "x" cm

So base of triangle = 12 + (2 height ) = 2x + 12

On substituting the given value of area and assumed values of height and base in above formula we get

We can find solution of this equation using quadratic formula.

According to quadratic formula for general equation   solution of the equation is given by

Our equation is

So in our case, a = 1 , b = 6 and c = -51

On applying quadratic formula we get

As dimensions of triangle cannot be negative so neglect negative value

Height of triangle = x =  4.745 cm

Base of  triangle = 12 + ( 2 x 4.745  ) = 12 + 9.49 = 21.49 cm

Hence base and height of the triangle whose area is 51 and base of a triangle is twelve more than twice its height are 21.49 cm and 4.745 cm respectively.

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