Question

which shape has a larger area: a rectangle that is 7 inches by 3/4 inch, or a square with side length of 2 1/2 inches? show your reasoning.

Answer 1

Answer:

Square.

Explanation:

The surface formulae for a rectangle and a square are, respectively:

$A_{r} = w\cdot h$

$A_{s} = l^{2}$

The surfaces are computed herein:

$A_{r} = (7\,in)\cdot \left(\frac{3}{4}\,in\right)$

$A_{r} = \frac{21}{4}\,in^{2}$

$A_{s} = \left(\frac{5}{2}\,in\right)^{2}$

$A_{s} = \frac{25}{4}\,in^{2}$

Since $A_{s} > A_{r}$, the square has the largest area.

Answer 2

The rectangle has an area of- 5.25

and the square has an area of - 6.25

So the square has a larger area