Question

I will give you 30 points ? Need it quick please

Answer 1

Answer: x = 4 and length = 19 and width = 11


Step-by-step explanation:

(4x + 3)(4x - 5) = 209

I did guess and check:

Plug x = 2

(4(2) + 3)(4(2) - 5) = 209
(13)(3) = 209
39 is not equal to 209

Plug x = 3

(4(3) + 3)(4(3) - 5)
= 15 x 7
= 105 is not equal to 209

Plug x = 4

(4(4) + 3)(4(4) - 5)
= 19 x 11
= 209 is equal to 209

Therefore x = 4 is correct.

Find length:

4x + 3
4(4) + 3
= 19

Find width:
4x - 5
4(4) - 5
= 11

Answer 2

x = 4

Length = 19 feet

Width = 11 feet

Step-by-step explanation:

Area = Length x Width

Area = 209 ft²

Length = (4x + 3)

Width = (4x - 5)

Find:

x

Length

Width

Area = Length x Width

209 = (4x + 3) * (4x - 5)

209 = 16x² - 8x - 15

16x² - 8x - 15 = 209

16x² - 8x - 15 - 209 = 209 -209

16x² - 8x - 224 = 0

use quadratic equation to solve x:

-(-8) + sqrt( -8² - 4 * 16 * (-224))

x = --------------------------------------------

2 * 16

x = 4, x = -(7/2) ----therefore use x = 4

solve for L:

Length = (4x + 3)

Length = (4 * 4 + 3)

Length = 19 feet

solve for W:

Width = (4x - 5)

Width = (4 * 4 - 5)

Width = 11 feet

check:

Area = Length x Width

209 = (4x + 3) * (4x - 5)

Area = Length x Width

209 = 19 * 11

209 = 209 ----- OK