Problema Solution
Two rectangles have the game width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The longer rectangle has 5 more square feet than the smaller. What is the width of the rectangles.
Answer provided by our tutors
Let x=width
Length of one=x+1
Length of other=x+2
Area = Length times Width
Now we are told that:
x(x+2)=x(x+1)+4 clear parens
x^2+2x=x^2+x+4 subtract x^2 and x from both sides
x^2-x^2+2x-x=x^2-x^2+x-x+4 collect like terms
x=4 feet----------------width of the rectangles
x+1=4+1=5 feet--------- length of one
x+2=4+2=6 feet-----------length of the other
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Area of smaller=4*5=20 sq ft
Area of larger=4*6=24 sq ft
Larger is 4 more than smaller