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s344n2d4d5 [400]
3 years ago
6

A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the are

a remains the same. Find the area of the rectanel g. The ratio of two numbers is 2:5. If the larger number is 40, what is the smaller number h. Sixteen construction workers can finish cementing a floor of a building in 3 hours.
Mathematics
1 answer:
Katarina [22]3 years ago
6 0

Answer: Area = 6m²

              Smaller number = 16

              Hours = 9.6 h

Step-by-step explanation:

A rectangle is 5 meters longer than its width. If the length is shortened by 2 meters and width is increased by 1 meter, the area remains the same. Find the area of the rectangle.

1) w = x m                                2) w = x + 1 m

     l = x + 5  m                               l = x + 5 - 2 = x + 3 m

A₁ = A₂

A = w*l

A₁ = x(x+5) = x² + 5x

A₂ = (x+1)(x+2) = x² + x + 2x + 2 = x² + 3x + 2

A₁ = A₂

x² + 5x = x² + 3x + 2

5x - 3x = 2

2x = 2

x = 1

A₁ = x(x+5) = 1.6 = 6 m²

The ratio of two numbers is 2:5. If the larger number is 40, what is the smaller number.

<u> 2 </u> = <u> x </u>

5     40

5x = 80

x = 80/5 = 16

Sixteen construction workers can finish cementing a floor of a building in 3 hours. On a certain day, only 5 construction workers are available for the job. How long will it take the 5 construction workers to do the cementing job?

workers                      hours

    16                              3

     5                               x

↑                                          ↓              inversely proportional

<u> 5 </u> = <u> 3 </u>

16      x

5x = 16*3

5x = 48

x = 48/5

x = 9.6 h

 

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