Question

select the correct answer.
nancy is planting cucumbers in a small garden. before planting, nancy adds a layer of soil to the garden.
approximately how many square feet is needed to cover the garden with a layer of soil?
a. 98
b. 73.5
c. 49
d. 147

Explanation:

Step1: Identify the type of triangle

The triangle is a \(45^{\circ}-45^{\circ}-90^{\circ}\) right - angled triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the legs are equal. Let the length of each leg be \(a\). The hypotenuse \(c\) is related to the leg by the formula \(c = a\sqrt{2}\). Given \(c = 14\) ft, then \(a=\frac{c}{\sqrt{2}}=\frac{14}{\sqrt{2}}=\frac{14\sqrt{2}}{2}=7\sqrt{2}\) ft.

Step2: Calculate the area of the triangle

The area of a right - angled triangle is \(A=\frac{1}{2}\times base\times height\). Since base \(a = 7\sqrt{2}\) ft and height \(a = 7\sqrt{2}\) ft, \(A=\frac{1}{2}\times(7\sqrt{2})\times(7\sqrt{2})\).

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Answer:

C. 49