Point E is on side AB of rectangle ABCD. If the area of ABCD is 48, what is the area of triangle CDE?

CDE is a triangle has the same base b and the same height h as the rectangle.

Its area is therefore bh/2.

The area of the rectangle is bh=48.

So what is the area of the triangle?

169

To find the area of triangle CDE, we first need to determine the length of side CD. Since ABCD is a rectangle, opposite sides are equal in length. So, the length of side CD is equal to the length of side AB.

Next, we need to find the length of side CD. We can do this by considering the area of the rectangle ABCD. We know that the area of a rectangle is given by the product of its length and width. Therefore, the length of side CD can be found by dividing the area of the rectangle by the length of side AB.

Given that the area of ABCD is 48, we have:

48 = AB * CD

Since we know that CD = AB, we can substitute CD with AB:

48 = AB * AB

We can solve this equation to find the length of side AB. Taking the square root of both sides gives:

sqrt(48) = sqrt(AB * AB)

Simplifying further:

sqrt(48) = AB

Therefore, the length of side AB is equal to the square root of 48.

Now that we have the length of side CD (which is the same as the length of side AB), we can proceed to calculate the area of triangle CDE.

The area of a triangle can be calculated using the formula:

Area = (base * height) / 2

In this case, CD is the base of the triangle and DE is the height. So, we can substitute these values into the formula to find the area of triangle CDE:

Area of triangle CDE = (CD * DE) / 2

Since CD = AB and DE = CD, we can substitute these values into the formula:

Area of triangle CDE = (AB * CD) / 2

Area of triangle CDE = (AB * AB) / 2

Now that we know the length of side AB (which is the same as the length of side CD), we can calculate the area of triangle CDE by substituting this value:

Area of triangle CDE = (sqrt(48) * sqrt(48)) / 2

Simplifying this expression gives us the final answer: the area of triangle CDE.