A rectangle with an area of 456 square millimeters has a length and width in a ratio of 19:6. What are the length and width?length = millimeterswidth = millimetersSubmit
Question
A rectangle with an area of 456 square millimeters has a length and width in a ratio of 19:6. What are the length and width?length = millimeterswidth = millimetersSubmit
Solution
The area of a rectangle is given by the formula: Area = Length * Width
We know that the area is 456 square millimeters and the ratio of length to width is 19:6.
Let's denote the common ratio as x. So, the length is 19x and the width is 6x.
Substituting these into the area formula gives us:
456 = 19x * 6x 456 = 114x^2
Solving for x gives us:
x^2 = 456 / 114 x^2 = 4 x = sqrt(4) x = 2
Substituting x = 2 back into the expressions for length and width gives us:
Length = 19x = 192 = 38 millimeters Width = 6x = 62 = 12 millimeters
So, the length of the rectangle is 38 millimeters and the width is 12 millimeters.
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