Problem 15 · 2020 Math Kangaroo
Medium
Geometry & Measurement
Fractions, Decimals & Percents
area-fraction
The garden of Sonia's house is shaped like a 12-meter square and is divided into three lawns of equal area. The central lawn is shaped like a parallelogram whose shorter diagonal is parallel to two sides of the square, as shown in the picture. What is the length of this diagonal, in meters?
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Answer: C — 8.0
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Hint 1 of 2
The square's area is 12 × 12 = 144, split into three equal lawns of 48 each.
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Hint 2 of 2
The central parallelogram has its short diagonal horizontal; its area is half that diagonal times the full height 12.
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Approach: use the equal-thirds area
- Total area 12 × 12 = 144, so each lawn has area 144 ÷ 3 = 48.
- The central parallelogram spans the full 12 m height, and its area equals (diagonal × 12) ÷ 2.
- So 48 = (d × 12) ÷ 2, giving d = 8.
- The diagonal is 8.0 m, choice C.
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