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.

Question

Aimee Hogan

Mathematics

7 October, 06:02

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.

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Answers (1)

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Butterball · Answer 1

Hello,

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)

(20,50)

2*20+50=90 (cm)

20*50=1000 (cm²)