SOLUTION: the base and height of a triangle are (x+3)cm and (2x+5)cm respectively if the area of a triangle is 20 cm square , find x

Question 709684: the base and height of a triangle are (x+3)cm and (2x+5)cm respectively if the area of a triangle is 20 cm square , find x
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
the base and height of a triangle are (x+3)cm and (2x+5)cm respectively if the area of a triangle is 20 cm square , find x
.
Since area of a triangle is:
(1/2)bh = area
plugging in the given data:
(1/2)(x+3)(2x+5) = 20
multiplying both sides by 2:
(x+3)(2x+5) = 40
FOIL the left:
2x^2+5x+6x+15 = 40
2x^2+11x+15 = 40
2x^2+11x-25 = 0
applying the "quadratic equation" we get:
x = {1.73, -7.23}
.
details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=321 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.72911821679223, -7.22911821679223. Here's your graph:

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