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### This Is a Certified Answer

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The area of a rectangular library room is 60 squared meter. Find the perimeter of the room given that its length is 3 meter more than thrice its width.

Representation:

Let width = x meter

length = 3x + 3 meter

Area = 60 m²

Area of Rectangle = Length × Width

60 = (3x+3) (x)

60 = 3x² + 3x

Equate to zero (this a quadratic equation)

3x² + 3x - 60 = 0

Solve by factoring:

3 (x² + x + 20) = 0

3 (x-4) (x+5) = 0

x-4 = 0 x + 5 = 0

x = 4 x = -5

Choose the positive value x = 4

Width: x = 4 meters

Length: 3x + 3

= 3(4) + 3

= 12 + 3

= 15 meters

Perimeter of a rectangle: 2 (L) + 2 (W)

P = 2 (15 meters) + 2 ( 4 meters)

P = 30 meters + 8 meters

P = 38 meters

The perimeter of the rectangular library room is 38 meters.

Representation:

Let width = x meter

length = 3x + 3 meter

Area = 60 m²

Area of Rectangle = Length × Width

60 = (3x+3) (x)

60 = 3x² + 3x

Equate to zero (this a quadratic equation)

3x² + 3x - 60 = 0

Solve by factoring:

3 (x² + x + 20) = 0

3 (x-4) (x+5) = 0

x-4 = 0 x + 5 = 0

x = 4 x = -5

Choose the positive value x = 4

Width: x = 4 meters

Length: 3x + 3

= 3(4) + 3

= 12 + 3

= 15 meters

Perimeter of a rectangle: 2 (L) + 2 (W)

P = 2 (15 meters) + 2 ( 4 meters)

P = 30 meters + 8 meters

P = 38 meters

The perimeter of the rectangular library room is 38 meters.

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

**Two consecutive numbers have a sum of 47. What are the numbers?**

**Representation**: Let x = 1st number

x + 1 = 2nd number

**Equation**: x + (x + 1) = 47

**Solution**: x + (x + 1) = 47

x + x + 1 = 47

2x + 1 = 47

2x = 47 - 1

2x 46

---- = ---- ⇒

**x = 23 ; x + 1 = 24**

2 2

**Answer:**The two consecutive numbers are 23 and 24.

**Check:**x + (x + 1) = 47

23 + (23 + 1) = 47

23 + 24 = 47

47 = 47

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