A contractor bought a rectangular piece of land that has a perimeter of 200 feet. The ratio of the land's length to width is 9 : 16.

Length = 36feet

Width = 64 feet

Area = 2304 ft²

Step-by-step explanation:

Complete Question

A contractor bought a rectangular piece of land that has a perimeter of 200 feet. The ratio of the land's length to width is 9 : 16. Find the area of the land

Perimeter of the land = 2(L+W)

L is the length

W is the width

Given

Perimeter = 200 feet

If the ratio of the land's length to width is 9 : 16, then;

L/W = 9/16

9W = 16L

W = 16/9 L

Substitute into the formula

P = 2(L + 16/9 L)

P = 2(25L/9)

P = 50L/9

200 = 50L/9

1800 = 50L

L = 180/5

L = 36

Since W = 16/9 L

W = 16/9 * 36

W = 16 * 4

W = 64 feet

The area of the land = Length * Width

The area of the land = 36*64

The area of the land = 2304ft²

m∠a is 90°

m∠b is 40°