Gerald purchased a rectangular plot of land. the length of the plot is 20 feet more than the width. the cost of the land was $12

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Gerald purchased a rectangular plot of land. the length of the plot is 20 feet more than the width. the cost of the land was $12

per square foot. gerald also had a fence put around the entire perimeter of the plot, at a cost of s8 per linear foot. the total amount he spent on both the land and the fence was $10,560. part a write an equation in two variables for the perimeter, p, and an equation in two variables for the area, a, of the plot of land where x is the width of the plot in feet. provide evidence to support your equations

Mathematics

1 answer:

Maurinko [17] · Answer 1 · 2023-10-25T17:12:42+03:00

Answer:

P =2(x+ y) $ft$ .

A =xy $ft^{2}$

Step-by-step explanation:

perimeter of rectangle (P)= 2(L+B

Area of rectangle (A) = L×B

Given,

width = 'x'

length = y = x+20

therefore using above formula

P = 2(x+20 + x) = 2(2x+20)

A = (x+20)(x)

cost of land per square foot = $12

cost of land per linear foot = $8

total cost of land = $10560

now,

P×8 + A×12 = 10560

2(2x+20)×8 + (x+20)(x)×12 = 10560

32x + 320 + 12x²+ 240x = 10560

12x² + 272x = 10240

12x² + 272x - 10240 = 0

solving this quadratic equation using Discriminant method

x = [-b ±√(b² - 4ac)]/2

where b is the coefficient of x

a is the coefficient of x²

and c is the constant term

by replacing values in the above formula

x = 19.5 , x = -42.24

as the area cannot be negative therefore -42.24 is neglected

hence x = 19.5ft