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Chapter 5: Problem 57

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 the triangle

First, verify if the triangle is a right triangle using Pythagoras' theorem. In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the square of the lengths of the other two sides. Here, \(200^2 + 500^2 = 600^2\), so it's a right triangle.
02

Identify the base and height of the triangle

In right triangles, any of the two sides forming the right angle can be taken as base and height. So, the length of 500 feet and 200 feet will be taken as the base and the height.
03

Calculate the area of the triangle

Now that the triangle has been identified as right triangle and we have the base and height, we can calculate the area of the triangle using the formula \(Area = 0.5 \times base \times height\). Substituting the provided lengths, we get the area as \(Area = 0.5 \times 500 feet \times 200 feet\) which is 50000 square feet.

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