Question

a rectangle has a width of x meters and a length of x + 4 meters. if the area is 60 m², what is the value?

Explanation:

Step1: Write area formula

The area formula for a rectangle is $A = length\times width$. Given width $=x$ and length $=x + 4$ and $A=60$, we get the equation $x(x + 4)=60$.

Step2: Expand the equation

Expand $x(x + 4)$ to get $x^{2}+4x=60$, then rewrite it as the quadratic - equation $x^{2}+4x−60 = 0$.

Step3: Factor the quadratic equation

We factor $x^{2}+4x−60$ as $(x + 10)(x - 6)=0$.

Step4: Solve for x

Set each factor equal to zero: $x+10 = 0$ gives $x=-10$ and $x - 6=0$ gives $x = 6$. Since the width of a rectangle cannot be negative, we discard $x=-10$.

Answer:

A. 6