crossing the boarder
Geometry
Level
2
A photograph is twice as long as it is wide. It is mounted so that a boarder 2cm wide completely surrounds the photograph. Find the dimensions of the photograph if the area of the boarder is 136 cm squared?
8 cm and 16cm
12.30 cm and 24.60cm
15 cm and 30 cm
10 cm and 20 cm
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1 solution
The trick to this problem is to realize the border adds 4cm on each the length and width measurement when including the border.
Area of the photo without border=length x width= 2 w × w = 2 w 2 where w is the width of the photo.
Area of the photo with border= ( 2 w + 4 ) × ( w + 4 ) = 2 w 2 + 1 2 w + 1 6 .
Area of the border=(Area of the photo with border)-(Area of the photo without border)= ( 2 w 2 + 1 2 w + 1 6 ) − ( 2 w 2 ) = 1 3 6 c m 2 ⇒ 1 2 w = 1 2 0 ⇒ w = 1 0
such that width=w=10 and length=2w=20.