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 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.

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.

2 = x

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

5 = 3

16 x

5x = 16*3

5x = 48

x = 48/5

x = 9.6 h