Math Problem Statement

Find the perimeter of the figure. (All lines meet at right angles.) The total height of the figure is 92 cm, and the total width is 125 cm. The width of the smaller rectangle (B) is 33 cm.

Solution

The problem in the image asks to find the perimeter of a figure made up of rectangles, with all lines meeting at right angles. The lengths provided are:

  • Total height: 92 cm
  • Total width: 125 cm

The figure is divided into three sections labeled A, B, and C. However, the dimensions of the inner rectangles (B and C) are not completely provided. The width of B is 33 cm, which is written near the rectangle.

Let's break it down:

  • The total width of the figure is 125 cm.
  • The total height of the figure is 92 cm.
  • The width of B is 33 cm, meaning the width of A is 12533=92125 - 33 = 92 cm.

To find the perimeter, we sum up all the outer sides:

  1. The height of the figure is 92 cm (on both left and right sides).
  2. The total width is 125 cm (top and bottom).

Thus, the perimeter PP is calculated as:

P=2×height+2×widthP = 2 \times \text{height} + 2 \times \text{width} P=2×92cm+2×125cmP = 2 \times 92 \, \text{cm} + 2 \times 125 \, \text{cm} P=184cm+250cm=434cmP = 184 \, \text{cm} + 250 \, \text{cm} = 434 \, \text{cm}

So, the perimeter of the figure is 434 cm.

Would you like further clarification or details on any part of this?

Here are 5 related questions for further practice:

  1. If the width of rectangle C was 40 cm, what would the width of A be?
  2. How would the perimeter change if the height increased to 100 cm?
  3. Can you find the area of the figure?
  4. How many total rectangles are needed to form a similar shape?
  5. If you were to remove the smaller rectangle B, what would the new perimeter be?

Tip: The perimeter only depends on the outer sides of the figure, not on the inner divisions of the shape.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter
Rectangles

Formulas

Perimeter of a rectangle: P = 2 × height + 2 × width

Theorems

Perimeter theorem for rectangular shapes

Suitable Grade Level

Grades 5-7