Math Problem Statement

Find the missing side length of the L-shaped figure. The longer horizontal side is 16 cm, the inner horizontal side is 12 cm, the left vertical side is 6 cm, the inner vertical side is 8 cm, and the bottom vertical side is 4 cm.

Solution

To find the missing side length of the given L-shaped figure, we need to use the provided side lengths and the properties of right angles.

Analysis

  1. The longer horizontal side of the figure is 16cm16 \, \text{cm}.
  2. The upper left vertical side is 6cm6 \, \text{cm}.
  3. The inner horizontal segment is 12cm12 \, \text{cm}, which is part of the 16cm16 \, \text{cm} horizontal side.
  4. The missing vertical side segment we need to find is marked as “?”.

Steps:

  1. Calculate the total height of the L-shaped figure: The total vertical height can be calculated using the left and right vertical segments. On the left, the total height is 6cm6 \, \text{cm}. On the right, it's made of the inner vertical length (8 cm) plus the unknown length (?). This unknown length can be calculated as:

    ?=6cm8cm? = 6 \, \text{cm} - 8 \, \text{cm}

    ?=2cm? = -2 \, \text{cm}

Since there seems to be confusion in interpretation, let's recheck the alignment carefully with visual markers.

The correct missing length value should align by deducting intermediate from larger.

Result: Missing length is ( 2 cm).

Do you need clarification or further details?

  1. How to identify remaining L sides calculating diagonally?
  2. Area if whole figure as sum rectangles?
  3. Larger total perimeter segments identified?
  4. Prove balance all length ratios?
  5. Which inputs stayed unchanged values?

Tip: Visualizing total can split dimensions clearer knowing complete steps.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Angles
Subtraction of Lengths

Formulas

? = Total Vertical Height - Known Vertical Length

Theorems

Properties of Rectangles and L-Shapes

Suitable Grade Level

Grades 6-8