Question

nancy is planting cucumbers in a small garden. before planting, nancy adds a layer of soil to the gard
image of a right isosceles triangle with hypotenuse 14 ft and two 45° angles
approximately how many square feet is needed to cover the garden with a layer of soil?
a. 98
b. 49
c. 73.5
d. 147

Explanation:

Step1: Identify triangle type

It is a 45-45-90 right triangle (isosceles right triangle), so legs are equal. Hypotenuse = $14$ ft.

Step2: Find leg length

For 45-45-90 triangle: hypotenuse = leg $\times\sqrt{2}$. So leg = $\frac{14}{\sqrt{2}} = 7\sqrt{2}$ ft.

Step3: Calculate area

Area = $\frac{1}{2}\times$ leg $\times$ leg = $\frac{1}{2}\times(7\sqrt{2})^2 = \frac{1}{2}\times98 = 49$ sq ft.

Answer:

B. 49