Question

A rectangular parcel of land has an area of 8,000 ft2. a diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. what are the dimensions of the land, correct to the nearest foot? ft (smaller value) by ft (larger value)

Answer 1

Answer:

Step-by-step explanation:

Let the area of the rectangle be Length × width

LW = 8000

If the diagonal is 10feer greater than one of its length then:

D = 10+L

Diagonal is represented using the Pythagoras theorem as shown:

D² = L²+W²

(10+L)²= L²+W²

100+20L +L² = L²+W²

From LW = 8000

W = 8000/L

100 + 20L = (8000/L)²

100 +20L = 64,000,000/L²

Cross multiply

100L² + 20L³ = 64,000,000

2L³+10L² = 6,400,000

L³+5L² = 3200000

L³+5L² -3200000 = 0

Answer 2

Answer:

55 ft by 146 ft

Step-by-step explanation:

Given the following :

Area of rectangle = 8000 ft^2

Area of rectangle = length(L) * width(W)

Let length of a side = x

Length of side 2 = 8000 / x

Diagonal = 10 feet longer than one side = (x + 10)

The diagonal is the hypotenus = (x + 10)²:

Hyp² = (8000/x)² + x²

(x + 10)² = (8000/x)² + x²

x² + 20x + 100 = 64,000,000 / x² + x²

20x + 100 = 64,000,000 / x²

(20x + 100) * x² = 64,000,000

20x³ + 100x² - 64,000,000 = 0

x³ + 5x² - 3200000 = 0

Using calculator

x = 145. 71 = 146 ft

8000 / x

8000/145.71

= 54.9 ft

= 55ft

55ft by 146 ft