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

Question

AAABBBCCCDDD2524Calculate the perimeter of the rectangle ABCD.

Video Solution

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