The length of a rectangle is 11 cm less than 3 times its width. If the area of the rectangle is 20 square inches, find the length and width
1 sq inch = 6.4516 sq centimeters
6.4516 * 20 = 129.032 sq. centimeters
Can you take it from there?
To find the length and width of the rectangle, we can use algebraic equations based on the given information.
Let's assume the width of the rectangle is "w" cm. According to the problem, the length of the rectangle is 11 cm less than 3 times its width, which can be written as:
Length = 3w - 11
The formula for the area of a rectangle is length times width. Given that the area is 20 square inches, we can write the equation:
Length × Width = 20
Substituting the expressions for length and width from above, we have:
(3w - 11) × w = 20
Now, we can solve this equation to find the value of "w" (width) and then use it to find the value of "length."
Expanding the equation, we get:
3w² - 11w = 20
Rearranging the equation, we have:
3w² - 11w - 20 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
After solving the equation, we find that w = 5 or w = -8/3. Since we're dealing with lengths, the width cannot be negative or a fraction in this context. Therefore, we discard the solution w = -8/3.
Hence, the width of the rectangle is 5 cm. To find the length, we can substitute this value back into one of the earlier equations:
Length = 3w - 11
Length = 3(5) - 11
Length = 15 - 11
Length = 4 cm
Therefore, the length of the rectangle is 4 cm, and the width is 5 cm.