Word Problems: Quadratic Equations
Quadratic equationsarequadratic functionsthat are set equal to a value. A quadratic equation is an equation that can be written in the standard form, whereandare integers.
The quadratic equations are very useful in real world situations. Here we see an example of finding the lengths of a right triangle.
Example :
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 thehypotenuseof the right triangle.
Letbe the length of the shorter leg. The three sides are formed by three consecutive even integers. So,be the length of the longer leg andbe the length of the hypotenuse.
Simplify.
Write in standard form.
Now factor the trinomial.
Find two numbers so that the product isand their sum is.
The numbers areand.
Solve each equation.
Since the length of the triangle cannot be negative, the value ofis. So, the length of the shorter leg isft.
The length of the longer leg isorft and the hypotenuse isorft.