Calculate the Perimeter of Rectangle ABCD with Sides 24 and 25 Units

Question

AAABBBCCCDDD2524Calculate the perimeter of the rectangle ABCD.

Video Solution

Solution Steps

00:00 Calculate the perimeter of the rectangle
00:04 Let's use the Pythagorean theorem in triangle BCD
00:10 We'll substitute appropriate values and solve for BC
00:19 Let's isolate BC
00:30 This is the length of side BC
00:33 The perimeter of the rectangle equals the sum of its sides
00:38 Opposite sides in a rectangle are equal, so multiply by 2 for each side
00:42 And this is the solution to the problem

Step-by-Step Solution

Let's focus on triangle BCD in order to find side BC.

We'll use the Pythagorean theorem using our values:

BC2+DC2=BD2 BC^2+DC^2=BD^2

BC2+242=252 BC^2+24^2=25^2

BC2=625576=49 BC^2=625-576=49

Let's now remove the square root:

BC=7 BC=7

Since each pair of opposite sides are equal to each other in a rectangle, we can state that:

DC=AB=24 DC=AB=24

BC=AD=7 BC=AD=7

Now we can calculate the perimeter of the rectangle by adding all sides together:

24+7+24+7=14+48=62 24+7+24+7=14+48=62

Answer

62