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Chapter 5: Problem 59

The lengths of the sides of a triangular parcel of land are approximately 200 feet, 500 feet, and 600 feet. Approximate the area of the parcel.

Short Answer

Expert verified
The area of the triangular parcel of land is 50,000 square feet.

Step by step solution

01

Identify the type of triangle

Check if the triangle with side lengths 200 feet, 500 feet, and 600 feet is a right triangle by using the Pythagorean Theorem \(a^{2} + b^{2} = c^{2},\) where \(c\) is the hypotenuse. Substitute the values into the theorem: \(200^{2} + 500^{2} = 600^{2}.\) If this equation is correct, then it's a right triangle.
02

Calculate Area Using Redefined Formula

Since it's confirmed that this is a right triangle, we now use the formula for the area of a right triangle, which is \((1/2) \times \text{base} \times \text{height}.\) The base and the height is 200 feet and 500 feet respectively.
03

Compute the area

Substitute the base (200 feet) and the height (500 feet) into the area formula: \((1/2) \times 200 \times 500\). Multiply these values together to get the area in square feet.

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