Nancy is planting cucumbers in a small garden Before planting, Nancy adds a layer of soil to the gar Approximately how many square feet is needed to cover the garden with a layer of soil? A. 73.5 B. 147 C. 49 D. 98

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Nancy is planting cucumbers in a small garden Before planting, Nancy adds a layer of soil to the gar Approximately how many square feet is needed to cover the garden with a layer of soil? A. 73.5 B. 147 C. 49 D. 98

Answer 1

To find the area that Nancy needs to cover with a layer of soil, we need to calculate the area of the isosceles right triangle.Step 1: Use the Pythagorean theorem to find the length of the legs of the triangle.Since the triangle is an isosceles right triangle, both legs (let's call them 'a') are of equal length, and the hypotenuse (let's call it 'c') is 14 ft. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides:\[c^2 = a^2 + a^2\]\[14^2 = 2a^2\]\[196 = 2a^2\]\[a^2 = \frac{196}{2}\]\[a^2 = 98\]\[a = \sqrt{98}\]\[a = 7\sqrt{2} \text{ ft}\]Step 2: Calculate the area of the triangle.The area (A) of a triangle is given by the formula:\[A = \frac{1}{2} \times \text{base} \times \text{height}\]Since the base and height are the same in an isosceles right triangle (both are 'a'), we can write:\[A = \frac{1}{2} \times a \times a\]\[A = \frac{1}{2} \times (7\sqrt{2}) \times (7\sqrt{2})\]\[A = \frac{1}{2} \times 49 \times 2\]\[A = \frac{1}{2} \times 98\]\[A = 49 \text{ square feet}\]Therefore, the area that needs to be covered with a layer of soil is 49 square feet.The final answer is:C. 49

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Nancy is planting cucumbers in a small garden Before planting, Nancy adds a layer of soil to the gar Approximately how many square feet is needed to cover the garden with a layer of soil? A. 73.5 B. 147 C. 49 D. 98

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