Question

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.

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)