A square painting canvas has sides of length 45cm. A painter masks off a rectangular area on the canvas. She uses 90cm of tape to mask 3 sides of the rectangle and the 4th side is formed by 1 edge of the canvas. The area enclosed in the rectangle is 1000cm^2. Work out the length of the shorter sides of the rectangle.
Let's work in dm and dm². Let's a the shortest side
2a+b=9 ab=10 ==>2a²-9a+10=0 ==>(a=5/2 and b=4) or (a=2 and b=5) The rectangle is 25 cm * 40 cm or 20 cm * 50 cm Proof: (25,40) 2*25+40=90 (cm) 25*40=1000 (cm²)
