Calculate Rectangle Perimeter: Finding the Distance Around a 6 by 10 Shape

Video Solution

Solution Steps

00:00 Find the perimeter of the rectangle

00:03 Let's use the Pythagorean theorem in triangle BCD

00:17 Substitute appropriate values according to the given data and solve for DC

00:30 Isolate DC

00:45 This is the value of side DC

00:50 Opposite sides are equal in a rectangle

01:04 The perimeter of the rectangle equals the sum of its sides

01:13 Substitute appropriate values and solve for the perimeter

01:37 And this is the solution to the question

Step-by-Step Solution

Let's solve for the perimeter of the rectangle by following these steps:

First, identify the given information: The diagonal $AC$ is 10 units and the height $BC$ is 6 units.
Next, use the Pythagorean theorem to calculate the missing side (the base), $AB$ . Given that $AB^2 + BC^2 = AC^2$ , we can write:
Step 1: Substitute known values into the equation: $AB^2 + 6^2 = 10^2$ .
Step 2: Calculate $AB^2$ :

AB^2 + 36 = 100\\ AB^2 = 100 - 36\\ AB^2 = 64\\ AB = \sqrt{64} = 8

We have found the base $AB = 8$ units.

Now, calculate the perimeter $P$ using the perimeter formula $P = 2(l + w)$ , where $l$ is the length (AB = 8) and $w$ is the width (BC = 6).

P = 2(8 + 6) = 2 \times 14 = 28

Therefore, the perimeter of the rectangle is 28 units.

The correct choice is 3: 28.