Marisol is painting on a piece of canvas that has an area of 180 square inches. The length of the Painting is 1 1/4 times the width. What are the dimensions of the painting
x * (5/4)x = 180
x^2 = 144
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To find the dimensions of the painting, we can set up an equation based on the given information.
Let's assume the width of the painting is "w" inches.
According to the given information, the length of the painting is 1 1/4 times the width, which is equivalent to (1 + 1/4) times the width, or 5/4 times the width. Therefore, the length of the painting can be represented as (5/4)w inches.
We also know that the area of the painting is 180 square inches. The formula for finding the area of a rectangle is length × width. So, we can set up the following equation:
Area = length × width
180 = (5/4)w × w
To solve this equation, we can first simplify it:
180 = (5/4)w^2
Next, we can multiply both sides of the equation by 4/5 to isolate w^2:
(4/5) × 180 = w^2
(4 × 180) / 5 = w^2
(720) / 5 = w^2
144 = w^2
Now, we can take the square root of both sides to solve for w:
√144 = √(w^2)
12 = w
So, the width of the painting is 12 inches.
To find the length, we can substitute the value of w back into our previous equation:
length = (5/4)w
length = (5/4) × 12
length = 15 inches
Therefore, the dimensions of the painting are 12 inches for the width and 15 inches for the length.