A picture, together with its frame, makes a square of side length 80 cm. The frame is 4 cm wide.
What percentage of the area of the square is covered by the frame?
A. 15% B. 18% C. 19% D. 20% E. 24%
C. 19%
The horizontal edges of the frame are rectangles with dimensions 4 cm × 80 cm. Hence they each have area (4 × 80) cm2.
The vertical edges of the frame are rectangles with dimensions 4 cm × (80 − 2 × 4) cm, that is,4 cm × 72 cm.
Hence they each have area (4 × 72) cm2. Therefore the total area of the frame is (2× (4×80)+2× (4×72))cm2 =(2×4× (80+72))cm2.
The area of the square is (80 × 80) cm2. Therefore the percentage of the area of the square covered by the frame is ((2 × 4 × (80 + 72)) / (80 × 80)) ×100% =(10 + 9)/(10 × 10) ×100% = 19%
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