Malcom designed the roof plan of a house and implement shed. The dimensions of the house's roof are 25 ft wide by 40 long. The length of the shed's roof is 140 feet. If the two shapes are similar, what is the width of the shed's roof?

To find the width of the shed's roof, we can use the concept of similar shapes.

The given dimensions of the house's roof are 25 ft wide by 40 ft long. Let's assume that the shed's roof is also rectangular with a width of 'w' feet.

Since the two roofs are similar, the ratios of corresponding sides will be equal. In this case, we can set up the following proportion:

Width of the house's roof / Width of the shed's roof = Length of the house's roof / Length of the shed's roof

Using the given values, we can substitute them into the proportion:

25 ft / w ft = 40 ft / 140 ft

To solve for 'w', we cross-multiply and solve the resulting equation:

25 ft * 140 ft = 40 ft * w ft

3500 ft^2 = 40w

Now, divide both sides of the equation by 40 to isolate 'w':

3500 ft^2 / 40 = w

Simplifying,

87.5 ft = w

Therefore, the width of the shed's roof is 87.5 feet.