Problem 9 · 2017 Math Kangaroo
Medium
Geometry & Measurement
area-fraction
A rectangle is twice as long as it is wide. What fraction of the rectangle is shaded grey?
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Answer: B — \(\tfrac38\)
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Hint 1 of 2
Slice the rectangle along its diagonals and midline and compare the shaded triangles to the whole.
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Hint 2 of 2
Add up the grey pieces as a fraction of the full rectangle.
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Approach: split the rectangle into two equal squares and add the grey pieces
- The rectangle is twice as long as wide, so it splits down the middle into two equal squares.
- In the left square the grey is one triangle that is exactly half the square.
- In the right square the grey triangle is half of a half, so a quarter of that square.
- Grey is \(\tfrac12 + \tfrac14 = \tfrac34\) of one square, out of the two squares, so the shaded fraction is \(\tfrac34 \div 2 = \tfrac38\) — option (B).
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