SOLUTION: A rectangle is 4 times as long as it is wide. A second rectabgle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square cent
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Question 189049This question is from textbook Structure and Method Book 1
: A rectangle is 4 times as long as it is wide. A second rectabgle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the dimensions of the original rectangle? This question is from textbook Structure and Method Book 1
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Let w be the width of the smaller rectangle. Then the length of the smaller rectangle must be 4w. Also, the width of the larger rectangle must be w + 2 and the length of the larger rectangle must be 4w + 5.
Since the area of a rectangle is given by multiplying the length times the width, the smaller rectangle must have an area:
And the larger rectangle must have an area:
Since the area of the larger rectangle is 270 square centimeters greater than the area of the smaller rectangle, we can say:
Solve the equation for w to get the width of the original rectangle and then compute the length directly. To check your work, you need to compute the length and width of the larger rectangle as well, then compute the areas of the two rectangles to verify that the difference is 270 square centimeters.
