ABCD is a rectangle of perimeter 48cm. AB=6 cm and CD=DE. What is the length of ABCD?
Where did E come from?
6cm x 18cm=108cm Squared
To find the length of the rectangle ABCD, we can use the information given about its perimeter and the lengths of its sides.
The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the perimeter of ABCD is given as 48 cm. We can write the equation for the perimeter as:
P = 2*(AB + BC + CD + DA)
Let's substitute the known values into the equation:
48 = 2*(6 cm + BC + CD + 6 cm)
Simplifying further:
48 = 2*(12 cm + BC + CD)
Now, we know that CD = DE, so we can replace CD with DE in our equation:
48 = 2*(12 cm + BC + DE)
Dividing both sides of the equation by 2:
24 = 12 cm + BC + DE
Since we are given that AB = 6 cm, and we know that the opposite sides of a rectangle are equal, we can conclude that BC = AB = 6 cm.
Substituting this into our equation:
24 = 12 cm + 6 cm + DE
24 = 18 cm + DE
Subtracting 18 cm from both sides:
6 = DE
Therefore, the length of ABCD is DE, which is equal to 6 cm.