Question

dr. chavez drew a rectangle on a coordinate plane to estimate the size of a lake. each unit on the plane represents 1 mi. the coordinates of the rectangle are at the origin, (0,7), (12,7), and (12,0). based on this information, what is the perimeter of the lake? 38 miles 25 miles 7 miles 12 miles

Explanation:

Step1: Find the length and width of the rectangle

The length of the rectangle can be found by the difference in the \(x -\)coordinates. For points \((0,7)\) and \((12,7)\), the length \(l=|12 - 0|=12\) miles.
The width of the rectangle can be found by the difference in the \(y -\)coordinates. For points \((0,7)\) and \((0,0)\), the width \(w = |7-0|=7\) miles.

Step2: Use the perimeter formula for a rectangle

The perimeter formula of a rectangle is \(P=2(l + w)\).
Substitute \(l = 12\) and \(w=7\) into the formula: \(P=2(12 + 7)\).
First, calculate the sum inside the parentheses: \(12+7 = 19\).
Then, multiply by 2: \(P=2\times19=38\) miles.

Answer:

38 miles