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a_sh-v [17]
3 years ago
8

The area of a rectangle is 42 ft squared, and the length of the rectangle is 5 ft more than twice the width. Find the dimensions

of the rectangle. length and width.​
Mathematics
2 answers:
stira [4]3 years ago
7 0

Answer:

<h3>Length = 12 ft</h3>

Width = \frac{7}{2} ft

Step-by-step explanation:

Given,

Area of rectangle = 42 \:  {ft}^{2}

Width = X

Length = 2x + 5

Now,

x(2x + 5) = 42

2 {x}^{2}  + 5x   = 42

2 {x}^{2}  + 5x - 42 = 0

2 {x}^{2}  + 12x - 7x - 42 = 0

2x(x + 6) - 7(x + 6) = 0

(2x  - 7)(x + 6) = 0

Either

2x - 7 = 0

2x = 0 + 7

2x = 7

x =  \frac{7}{2}

Or,

x + 6 = 0

x = 0 - 6

x =  - 6

Negative value can't be taken.

So, width = \frac{7}{2} ft

Again,

Finding the value of length,

Length = 2x + 5

2 \times  \frac{7}{2}  + 5

7 + 5

12

Length = 12 ft

DanielleElmas [232]3 years ago
4 0

Answer:

length = 12 ft, width = 3.5 ft

Step-by-step explanation:

w = width

l = length = 2w + 5

A = wl = w(2w + 5) = 42

2w² + 5w - 42 = 0

(w + 6)(2w - 7) = 0

w + 6 = 0, w = -6 (dimension cannot be negative)

2w - 7 = 0, w = 3.5

l = 2(3.5) + 5 = 12

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