Question

nancy is planting cucumbers in a small garden. before planting, nancy adds a layer of soil to the garden. 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. 147
b. 49
c. 73.5
d. 98

Explanation:

Step1: Identify the triangle type

The triangle is a \(45 - 45-90\) right - triangle. In a \(45 - 45-90\) triangle, the legs are equal. Let the length of each leg be \(a\). Using the Pythagorean theorem \(a^{2}+a^{2}=c^{2}\), where \(c = 14\) (hypotenuse). So \(2a^{2}=14^{2}=196\), then \(a^{2}=98\), \(a=\sqrt{49\times2}=7\sqrt{2}\).

Step2: Calculate the area of the triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). For a right - triangle, the base and height are the legs. Here \(base = height=a = 7\sqrt{2}\). So \(A=\frac{1}{2}\times(7\sqrt{2})\times(7\sqrt{2})\).

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Answer:

B. 49