Toni and Missy have rectangular-shaped vegetable gardens. The width of Missy’s garden is double the width of Toni’s garden. The area of Missy’s garden is the same as that of Toni’s garden. Which statement is true?

The length of Missy’s garden is double the length of Toni’s garden.

Missy’s garden has the same length as Toni’s garden.

The length of Missy’s garden is one-half of the length of Toni’s garden.

Missy’s garden has the same perimeter as Toni’s garden.

Question

Toni and Missy have rectangular-shaped vegetable gardens. The width of Missy’s garden is double the width of Toni’s garden. The area of Missy’s garden is the same as that of Toni’s garden. Which statement is true?

 The length of Missy’s garden is double the length of Toni’s garden.

 Missy’s garden has the same length as Toni’s garden.

 The length of Missy’s garden is one-half of the length of Toni’s garden.

 Missy’s garden has the same perimeter as Toni’s garden.

anonymous · Answer

First one,since the areas are the same, the dimensions  should be too

pfenn1 · Answer

Let w be the width of Toni's garden.  Then the width of Missy's garden is 2w. The area of Toni's garden $$A_T=wl_T$$The area of Missy's garden is $$A_M=2wl_M$$The areas of the two gardens are the same. $$A_T=A_M; \text{ so }wl_T=2wl_M$$This can be rearrange to show$$\frac{l_T}{l_M}=\frac{2w}{w}=2$$or $$l_M=\frac12l_T$$So, which statement is true?