The height of a triangle is 5 cm shorter than its base. if the area of the triangle is 25 cm2, find the height of the triangle.

Step-by-step explanation:

Let's call B at the base of the triangle and call h at the height of the triangle. Then we know that:

The height of a triangle is 5 cm shorter than its base. This means that:

.

 The area of the triangle is 25 cm²

By definition the area of a triangle is:

For this triangle we know that and . We substitute these values in the equation and solve for B.

Now we use the quadratic formula to solve the equation.

For an equation of the form the quadratic formula is:

In this case note that:  

Then:

The solutions are:

For this problem we take the positive solution.

Now we substitute the value of B in the equation to find the height h