   SEARCH HOME Math Central Quandaries & Queries  Question from Denise: In a rectangular garden a person says if I made that bed 2 feet wider and 3 feet longer it Would have been 64 sq,ft bigger. But if it had been 3 feet wider and two feet longer It would have been 68 sq.ft bigger. What is the length and width of the garden bed? Hi Denise,

Suppose the garden is $L$ feet long and $W$ feet wide. Its area is then $L W$ square feet.

if I made that bed 2 feet wider and 3 feet longer it would have been 64 sq,ft bigger.

If the width was $W +2$ feet and the length was $L + 3$ feet then its area would be $(W + 2)(L + 3)$ square feet. In this case the area would be $L W + 64$ square feet. Thus

$(W + 2)(L + 3) = LW + 64.$

Simplify.

If the garden had been 3 feet wider and 2 feet longer it would have been 68 sq.ft bigger.

This gives you a second equation in $L$ and $W.$

Solve the two equations for $L$ and $W.$

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.