Sally painted a picture that has an area of 480 square inches. The length of the painting is 1 1/5 its width. Which of the following could be the
dimensions of Sally’s painting?
A. 20 inches by 24 inches
B. 12 inches by 40 inches
C. 16 inches by 30 inches
D. 15 inches by 32 inches
width --- x
length --- (6/5)x
(6/5)x^2 = 480
x^2 = 400
x = √400 = 20
picture is 20 inches by 24 inches
To find the dimensions of Sally's painting, we need to use the given information about the area and the relationship between the length and width.
Let's set up an equation to solve for the dimensions:
Area = Length × Width
We know that the area is 480 square inches. Let's use A for area, L for length, and W for width:
A = L × W
Substituting the given area:
480 = L × W
The problem also states that the length is 1 1/5 times the width, or 6/5 times the width. So we have:
L = (6/5)W
Now we can substitute this expression for L in terms of W into our equation for area:
480 = (6/5)W × W
Let's simplify this equation:
480 = (6/5)W^2
To solve for W^2, we can multiply both sides by 5/6:
(5/6) × 480 = W^2
400 = W^2
Now take the square root of both sides to find W:
W = √400
W = 20
So the width of Sally's painting is 20 inches.
To find the length, we can use the relationship between the length and width:
L = (6/5)W
Substituting the value of W:
L = (6/5) × 20
L = 24
Therefore, the dimensions of Sally's painting are 24 inches by 20 inches.
Checking each option:
A. 20 inches by 24 inches - This is a match.
B. 12 inches by 40 inches - The length is not 1 1/5 times the width.
C. 16 inches by 30 inches - The length is not 1 1/5 times the width.
D. 15 inches by 32 inches - The length is not 1 1/5 times the width.
Thus, the answer is A. 20 inches by 24 inches.
A.
Explination:
Let x = width
Let (6/5)x = length (NOTE: 6/5 is the same as 1 1/5)
Area = width * length
480 square inches = x * (6/5)x
480 = (6/5)x^2 (NOTE: now use order of operations)
400 = x^2 (NOTE: take the square root of both sides, to cancel out the exponent)
20 = x
If x = width, then width = 20.
A is the only choice with 20 as the width.
1.2 * 20 = 24
1.2 * 12 = 14.4
1.2 * 16 = ?
1.2 * 15 = ?