Question

the length of the rectangle is 5 ft Less Than 3 times the width and the area of the rectangle is 50 feet squared. what is the length and the width of the rectangle?

Answer 1

We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.

$50 = w*(3w - 5)$

Expand the multiplication
$50 = 3w^2 - 5w$

Subtract 50 from both sides.
$0 = 3w^2 - 5w - 50$

We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.

Finally, we can plug this solution into the length formula we found earlier to solve for length.
$l = 3w - 5$

Plug in the solution to w.
$l = 3(5) - 5$

Multiply 3 and 5.
$l = 15 - 5$

Subtract 5
$l = 10$

Therefore the width is 5 and the length is 10.