Math Problem Statement

Moldes an architect built a model of a 220-foot tall building he is designing the molded is 25 inches tall and 10 inches wide how wide is the actually building

Solution

To solve this, we need to use the proportional relationship between the model's height and width and the actual building's height and width.

The model is 25 inches tall and represents a 220-foot tall building. Let's set up the proportion:

Model’s heightActual height=Model’s widthActual width\frac{\text{Model's height}}{\text{Actual height}} = \frac{\text{Model's width}}{\text{Actual width}}

Substitute the given values into the proportion:

25inches220feet=10inchesActual width in feet\frac{25 \, \text{inches}}{220 \, \text{feet}} = \frac{10 \, \text{inches}}{\text{Actual width in feet}}

Now, solve for the actual width:

Actual width in feet=10inches×220feet25inches=2200inch-feet25inches=88feet\text{Actual width in feet} = \frac{10 \, \text{inches} \times 220 \, \text{feet}}{25 \, \text{inches}} = \frac{2200 \, \text{inch-feet}}{25 \, \text{inches}} = 88 \, \text{feet}

So, the actual building's width is 88 feet.

Would you like further details or have any questions?

Here are 5 related questions:

  1. How would you calculate the actual building's length if the model's length is known?
  2. How do different unit conversions affect scale modeling calculations?
  3. If the model's height was increased by 10%, what would the new actual building height be?
  4. How can you find the area of the actual building's base from its width and length?
  5. How is a scale factor determined in architectural models?

Tip: Always ensure unit consistency when calculating proportions, converting all measurements to the same unit type.

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Math Problem Analysis

Mathematical Concepts

Proportions
Unit Conversion
Scale Models

Formulas

Model's height / Actual height = Model's width / Actual width
Cross-multiplication to solve for width

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 6-8