If steves garden had an area of 128 square feet, what would the length of his garden have to equal

Question

Mark decided to build a rectangular vegetable garden in his backyard that was 8 feet long and 4 feet wide. Steve liked Mark's garden so much he wanted to build a garden that was similar in shape but larger. If Steve's garden had an area of 128 square feet, what would the length of his garden have to equal? 

Answer 1

Mark's garden area is 32 square feet.

Steve's Garden at 128 square feet will be 4 times as large and similar in shape.

For similar polygons if ratio of sides is a:b then ratio of areas is a^2:b^2 or conversely, if ratio of areas is a^2:b^2, the ratio of the sides is a:b.

Since the ratio of the areas is 1:4, the ratio of the sides will be 1:2, so Steve's garden will be 16 feet long by 8 feet wide.