A triangle’s base is 5 cm more than its height of x cm. Find its height if the triangle’s area is 10 cm 2

The area of a triangle is given by the formula: Area = 1/2 * base * height

Given that the area is 10 cm^2, the base is x + 5 cm, and the height is x cm, we can substitute these values into the formula:

10 = 1/2 * (x + 5) * x

Solving this equation will give us the value of x, which is the height of the triangle.

First, we can simplify the equation by multiplying both sides by 2 to get rid of the fraction:

20 = (x + 5) * x

This simplifies to:

20 = x^2 + 5x

Rearranging the equation to set it equal to zero gives us:

x^2 + 5x - 20 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0, which can be solved using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this case, a = 1, b = 5, and c = -20.

Substituting these values into the quadratic formula gives:

x = [-5 ± sqrt((5)^2 - 41(-20))] / (2*1) x = [-5 ± sqrt(25 + 80)] / 2 x = [-5 ± sqrt(105)] / 2

The solutions to this equation are x = (-5 + sqrt(105)) / 2 and x = (-5 - sqrt(105)) / 2. However, since the height of a triangle cannot be negative, we discard the solution x = (-5 - sqrt(105)) / 2.

Therefore, the height of the triangle is x = (-5 + sqrt(105)) / 2 cm.