Rectangle Perimeter Calculation: Finding the Distance Around a 4x5 Shape

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the Pythagorean theorem to find the missing side.
• Step 3: Use the perimeter formula for rectangles.

Now, let's work through each step:

Step 1: The given information includes the base ($AB = 4$) and the diagonal ($AC = 5$).

Step 2: Apply the Pythagorean theorem. The diagonal acts as the hypotenuse of a right triangle with sides being the rectangle's base and height. Using the theorem:

$(AB)^2 + (AD)^2 = (AC)^2$

$4^2 + (AD)^2 = 5^2$

$16 + (AD)^2 = 25$

Solving for $(AD)^2$:

$(AD)^2 = 25 - 16 = 9$

Thus, $AD = \sqrt{9} = 3$.

Step 3: Calculate the perimeter using the formula for the perimeter of a rectangle:

$P = 2 \times (\text{length} + \text{width})$.

Inserting the values $AB = 4$ and $AD = 3$:

$P = 2 \times (4 + 3) = 2 \times 7 = 14$.

Therefore, the solution to the problem is $14$.