marisol is painting on a piece of canvas that has an area of 180 square inches. the lenght of the painting is 1 1/4 times the width. what are the dimensions of the painting
To find the dimensions of the painting, let's set up an equation based on the given information:
Let's assume the width of the painting is "x" inches. Therefore, the length of the painting would be 1 1/4 times the width, which can be expressed as (1 1/4) * x.
Since the area of the canvas is given as 180 square inches, we can set up the equation:
Width * Length = Area
x * ((5/4) * x) = 180
Next, simplifying the equation:
(5/4)x^2 = 180
To solve for x, the width of the painting, we need to isolate x by dividing both sides of the equation by (5/4):
x^2 = (180 / (5/4))
x^2 = 180 * (4/5)
x^2 = 144
Taking the square root of both sides gives us:
x = √144
x = 12
Now that we know the width of the painting is 12 inches, we can find the length by multiplying the width by 1 1/4:
Length = (1 1/4) * 12
Length = (5/4) * 12
Length = 15
Therefore, the dimensions of the painting are 12 inches in width and 15 inches in length.