Word Problems: Quadratic Equations
The quadratic equations are very useful in real world situations. Here we see an example of finding the lengths of a right triangle.
The three sides of a right triangle form three consecutive even numbers. Find the lengths of the three sides, measured in feet.
First assign a variable to one side of the triangle. The smaller value is the length of the shorter leg and the higher value is the hypotenuse of the right triangle.
Let be the length of the shorter leg. The three sides are formed by three consecutive even integers. So, be the length of the longer leg and be the length of the hypotenuse.
By Pythagorean Theorem , .
Write in standard form.
Now factor the trinomial.
Find two numbers so that the product is and their sum is .
The numbers are and .
Use zero product property .
Solve each equation.
Since the length of the triangle cannot be negative, the value of is . So, the length of the shorter leg is ft.
The length of the longer leg is or ft and the hypotenuse is or ft.