sarahc33
Answered

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The length of a rectangle is 5 ft more than twice the width, and the area of the rectangle is 63 ft^2. Find the dimensions of the rectangle.​

Sagot :

reinhard10158

Step-by-step explanation:

l = length

w = width

l = 2w + 5

l × w = 63

using the identity of the first equation in the second :

(2w + 5) × w = 63

2w² + 5w = 63

2w² + 5w - 63 = 0

the general solution to such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = w

a = 2

b = 5

c = -63

w = (-5 ± sqrt(5² - 4×2×-63))/(2×2) =

= (-5 ± sqrt(25 + 504))/4 = (-5 ± sqrt(529))/4 =

= (-5 ± 23)/4

w1 = (-5 + 23)/4 = 18/4 = 4.5 ft

we = (-5 - 23)/4 = -28/4 = -7

a negative Stilton does not make any sense for a side length, so, the only valid solution is w = 4.5 ft.

l = 2w + 5 = 2×4.5 + 5 = 9 + 5 = 14 ft

so,

the length = 14 ft

the width = 4.5 ft

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