The area of a rectangular wall of a barn is 32 square feet. It's length is 12 feet longer than twice it's width. Find the length and width if the wall of the barn.

Width = 2

Length  = 16

Step-by-step explanation:

lets start by writing everything we know

Area = 32 sqft

l = 2w + 12

l * w = 32

we can substitute l for 2w + 21 to figure what w equals

(2w + 12)w = 32

distribute the w

2w^2 + 12w = 32

2w^2 + 12w - 32 = 0

use quadratic formula to solve

w = -8, or 2

it can't be -8, so we will check with 2

2(2)^2 + 12(2) - 32 = 0

8 + 24 -32 = 0

32-32 = 0

l = 2(2) + 12

l = 4 + 12

l = 16

2*16 =32

Width = 2

Length  = 16

Question Asked: What type of number gets a math mathermatician in trouble the most when trying to use a function to model a real world situation?​

All numbers are imaginary. Introducing the square root(s) of minus one is convenient because all n-degree polynomials with real coefficients then have n roots, making algebra "complete"; it saves using matrix representations for objects that square to -1 (such objects representing an important part of the structure of linear equations which appear in quantum mechanics, heat diffusion, optics, etc). The hottest contenders for numbers without purpose are probably the p-adic numbers (an extension of the rationals), and perhaps the expiry dates on army ration packs.