Question

the length of a rectangle is 5 more than the width. the area is 150 square inches. find the length and width of the rectangle.

Explanation:

Step1: Let the width be $x$ inches.

The length is $x + 5$ inches.

Step2: Use the area formula for rectangle.

The area of a rectangle $A=length\times width$. So $150=(x + 5)\times x$, which simplifies to $x^{2}+5x-150 = 0$.

Step3: Factor the quadratic equation.

We factor $x^{2}+5x - 150=0$ as $(x + 15)(x - 10)=0$.

Step4: Solve for $x$.

Setting each factor equal to zero gives $x+15 = 0$ or $x - 10=0$. So $x=-15$ or $x = 10$. Since width cannot be negative, we take $x = 10$.

Step5: Find the length.

The length is $x + 5=10 + 5=15$ inches.

Answer:

Width = 10 inches
Length = 15 inches