Question

1. a new housing development extends 4 miles in one direction, makes a right turn, and then continues for 3 miles. a new road runs between the beginning and ending points of the development. what is the perimeter of the triangle formed by the homes and the road? what is the area of the housing development?

Explanation:

Step1: Find the length of the hypotenuse

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 4$ and $b=3$. So $c=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step2: Calculate the perimeter

The perimeter $P$ of a triangle is the sum of its side - lengths. $P=4 + 3+5=12$ miles.

Step3: Calculate the area

The area $A$ of a right - triangle is given by $A=\frac{1}{2}\times base\times height$. Here, base $= 4$ miles and height $= 3$ miles. So $A=\frac{1}{2}\times4\times3 = 6$ square miles.

Answer:

Perimeter: 12 miles
Area: 6 square miles