Substitute the information given into the rectangle area formula, then simplify.
Length: 18ft. Width: 8ft.
Practice makes perfect
When we are given the area of a rectangle, we generally need to use the formula for the area of a rectangle. In this case we need to write expressions for the length, l, and width, w.
Verbal Expression
Algebraic Expression
the length is 10 ft more than the width
l = 10 + w
Now that we have an algebraic expression, we can substitute. Then, let's see where we can go from there.
Now, we have a quadratic equation that is equal to zero. Let's look for two factors of -144 that have a sum of 10. Since ac is negative, the sign of the factors will be different. Furthermore, since b is positive, the factor with the larger magnitude will be positive too.
Factors
Sum of factors
-1, 144
143
-2, 72
70
-3, 48
45
-4, 36
32
-6, 24
18
-8, 18
10
We have found our factors that have a sum of 10. Since our leading coefficient is 1, we can use -8 and 18 directly as part of the factoring.
w^2 + 10w-144=(w-8)(w+18)
Let's set each factor equal to zero and solve for w.
Since w represents a measurement of distance, we can ignore the negative solution and say the width of the rectangle is 8 ft. To find the length, we can add 10 to the width and get 18ft.
