Question

A rectangle's length is 5 cm less than twice its width. If the length is decreased by 5 cm and width is increased by 2 cm, the perimeter of the resulting rectangular will be 74 cm. Find the length and the width of the original rectangle.

Answer 1

The length of the original rectangle is 29 cm and the width is 17 cm.

Step-by-step explanation:

To find the length and width of the original rectangle, we need to set up an equation based on the information given. Let's assume the width of the rectangle is x cm. Using the given information, we can set up the equation:

Length = 2x - 5
Width = x

The perimeter of the resulting rectangle is 74 cm, which means the sum of all four sides is 74 cm. The resulting rectangle has a length of (2x - 5) - 5 cm and a width of (x + 2) cm. We can set up the equation:

2((2x - 5) - 5) + 2(x + 2) = 74

Simplifying the equation:
4x - 20 - 10 + 2x + 4 = 74
6x - 26 = 74
6x = 100
x = 16.67

However, since the width of the rectangle cannot be a decimal value, we round x to the nearest whole number, which gives us x = 17 cm. Substituting this value back into our equations, we find that the length of the original rectangle is 2x - 5 = 2(17) - 5 = 34 - 5 = 29 cm.