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Question

A parcel of land is a rectangle that is 9 feet longer than it is wide. If the land is x feet wide, then it is............feet long and the length D of the diagonal can be written as a function of the width x of the parcel of land.

D =.................

Suppose each diagonal from one corner to the opposite corner is 45 feet long.

The parcel is..........feet by............feet. (smaller number first!)

Answer 1

A parcel of land is a rectangle that is 9 feet longer than it is wide. If the land is x feet wide, then it is x + 9 feet long and the length D of the diagonal can be written as a function of the width x of the parcel of land.

D = sqrt (x^2 + (x + 9)^2)

Suppose each diagonal from one corner to the opposite corner is 45 feet long.

The parcel is 27 feet by 36 feet. (smaller number first!)

Answer 2

Let x be the width, then x+9 = length
D the diagonal is the hypoteunuse: D = sqr[x^2 + (x+9)^2]
Now if x = 45 then
x^2 + (x+9)^2 = 45^2
x^2 + (x^2 + 18x + 81) = 2025
2x^2 + 18x - 1944 = 0
x^2 + 9x - 972 = 0
(x+36)(x-18) = 0
Therefore, x = 18, -36; but a negative number does not work so x = 18 the width, and x + 9 = 27 the length

Answer 3

lenght = width + 9 = x+9

diagonal = sqrt( width^2 + length ^2 )
= sqrt( x^2 + x^2 +18x +81)
= sqrt ( 2x^2 + 18x + 81)

if diagonal is 45 then
2x^2 + 18x + 81 = 2025
2x^2 + 18x -1944 = 0
x^2 + 9x -972 = 0
x = -4.5 + sqrt( 4.5^2 +972) = -4.5 + 31.5 = 27