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The length and width of a rectangle are in the ratio of 3:4. If the rectangle has an area of 108 square centimeters, what is the length of the diagonal?
A. 18 centimeters
B. 12 centimeters
C. 15 centimeters
D. 9 centimeters
E. 24 centimeters
Correct Answer: C
Explanation/Reference:
Explanation:
The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3x and 4x. We also know the area, so we write an equation and solve for x:
(3x)(4x) = 12x2 = 108.
x2 = 9 x = 3 Now we can recalculate the length and the width:
length = 3x = 3(3) = 9 centimeters width = 4x = 4(3) = 12 centimeters Using the Pythagorean Theorem we can find the diagonal, c:
length2 + width2 = c2
92 + 122 = c2
81 + 144 = c2
225 = c2
c = 15 centimeters
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