Question

The length of a rectangle is 4 units more than its width. The area of the rectangle is 25 more than 4 times the width. What is the width of the rectangle?

Answer 1

The length of a rectangle is 4 units more than its width:\[l=w+4\]

Answer 2

The area of the rectangle is 25 more than 4 times the width.
\[Area=4w+25\]

Answer 3

now we also know:\[Area=l \times w\\ \implies Area=\left( w+4 \right) \times w\ ...\ \{\because l=w+4\}\\ \implies Area=w^2+4w\]

Answer 4

next we set the 2 expressions for Area equal to each other, and solve:\[w^2+4w=4w+25\\ \implies w^2=25 \\ \implies w=\pm5\]And since the width can't be negative:\[width=5\]