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Chapter 3: Problem 47

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 approximate area of the triangular parcel of land is 50000 square feet.

Step by step solution

01

Identify the type of triangle

Find out if the given lengths form a Pythagorean triple by checking if they satisfy the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the greatest length. Here, use 200 feet and 500 feet as \(a\) and \(b\), and 600 feet as \(c\). Calculate \(a^2 + b^2\) and compare it to \(c^2\). If they equal, then the triangle is a right triangle.
02

Calculate the area

If the triangle is a right triangle, the area can be calculated by using the formula \(Area = 0.5 * base * height\). Here, use 500 feet for the base and 200 feet for the height, as it doesn't matter which one is the base, and which one is the height.
03

Result

The result is the area of the triangular parcel of land.

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