SOLUTION: The length and width of a rectangle are given by consecutive integers. The area of the rectangle is 12 cm^2. Approximate the length of a diagonal of the rectangle to three decimal

Algebra ->  Rectangles -> SOLUTION: The length and width of a rectangle are given by consecutive integers. The area of the rectangle is 12 cm^2. Approximate the length of a diagonal of the rectangle to three decimal       Log On


   

Question 712627: The length and width of a rectangle are given by consecutive integers. The area of the rectangle is 12 cm^2. Approximate the length of a diagonal of the rectangle to three decimal places.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x*(x+1) = 12

x^2 + x = 12

x^2 + x - 12 = 0

(x + 4)(x - 3) = 0

x + 4 = 0 or x - 3 = 0

x = -4 or x = 3

The two consecutive numbers are 3 and 4

a^2 + b^2 = c^2

3^2 + 4^2 = c^2

25 = c^2

c^2 = 25

c = sqrt(25)

c = 5

So the diagonal is 5 units long.