got a parallelogram ABCD = 100 sq in. AC=2 times BD. what is CD and BD? the diagonals AC divided into AE=2x and EC =2x, diagonal BD is divided into BE=x and ED=x. I got x=1. So line AC=2x or 4x? line BD=x or 2x? so, 100 sq in
0divided by 3x or 6x. Or did I goof?
To find the lengths of CD and BD in the given parallelogram, let's start by analyzing the given information:
1. The area of the parallelogram ABCD is given as 100 square inches.
2. The diagonal AC is twice the length of diagonal BD.
3. The diagonal AC is divided into AE = 2x and EC = 2x, where x represents a certain value.
4. The diagonal BD is divided into BE = x and ED = x.
From the given information, we can observe that AE + EC = AC, and AC is twice the length of BD. So we can write the equation:
2x + 2x = 2BD
Simplifying this equation gives us:
4x = 2BD
Dividing both sides by 2, we have:
2x = BD
So, BD is equal to 2x.
Now let's analyze the area of the parallelogram, which is given as 100 square inches. The formula to calculate the area of a parallelogram is base times height. In this case, the base can be considered as BD, and the height can be considered as CD.
Thus, we can write the equation:
BD * CD = 100
Substituting the value of BD as 2x, we get:
2x * CD = 100
Now, you mentioned that you obtained x = 1. Plugging this value into the equation, we have:
2(1) * CD = 100
Simplifying further, we find:
2 * CD = 100
Dividing both sides by 2, we get:
CD = 50
So, CD is equal to 50 square inches.
To summarize, based on the information given, we have found that BD is equal to 2x, where x = 1, meaning BD is equal to 2 inches. Furthermore, CD is equal to 50 inches.