The length of a rectangle is 5ft less than twice its width. The area of the rectanle is 75ft^2. Find the length of the rectangle
L = 2W-5
L * W = 75
Substitute 2W-5 for L in second equation and solve for W. Insert that value into the first equation and solve for L. Check by inserting both values into the second equation.
5ft
To find the length of the rectangle, we'll use the given information and solve step by step.
Step 1: Let's assume the width of the rectangle as 'w' feet.
Step 2: According to the given information, the length of the rectangle is 5 feet less than twice its width. Therefore, the length can be expressed as 2w - 5 feet.
Step 3: The formula for the area of a rectangle is length × width. We know that the area of the rectangle is 75 square feet. So, we can set up the equation:
(2w - 5) × w = 75
Step 4: Simplify the equation:
2w^2 - 5w = 75
Step 5: Rearrange the equation to have a quadratic equation form:
2w^2 - 5w - 75 = 0
Step 6: Factorize the quadratic equation:
(2w + 15)(w - 5) = 0
Step 7: Set each factor equal to zero and solve for 'w':
2w + 15 = 0 or w - 5 = 0
Step 8: Solve for 'w' in each equation:
w = -15/2 or w = 5
Since the width cannot be negative, we discard the solution w = -15/2.
Step 9: The width of the rectangle is 5 feet.
Step 10: To find the length, substitute the width value into the expression for the length:
length = 2w - 5
length = 2(5) - 5
length = 10 - 5
length = 5
Therefore, the length of the rectangle is 5 feet.