The area of a rectangle is 12 and the width is 3/4 the length. What are the dimensions?
3 by 4
To find the dimensions of a rectangle given the area and the relationship between its width and length, we can use algebra.
Let's assume the length of the rectangle is represented by "L".
Given that the width of the rectangle is 3/4 the length, we can express the width as (3/4)L.
The formula for the area of a rectangle is length multiplied by width: Area = Length × Width.
In this case, the area is given as 12, so we can write the equation:
12 = L × (3/4)L
Now, let's solve for L:
Multiply both sides of the equation by 4 to cancel out the denominator:
12 × 4 = L × (3/4)L × 4
48 = 3L²
Divide both sides of the equation by 3:
48/3 = 3L²/3
16 = L²
Take the square root of both sides:
√16 = √L²
4 = L
Therefore, the length of the rectangle is 4.
To find the width, we can substitute the length back into the equation for the width:
Width = (3/4)L = (3/4) × 4 = 3
So, the dimensions of the rectangle are length = 4 and width = 3.