The lengths of two sides of a parallelogram are 3 and 5. Which of the following is a possible value for the length if a diagonal if a parallelogram?

Are these your choices?

a.2
b.2
c.8
d.10
e.15

What is your answer?

My choices are:

A. 1
B. 4
C. 8
D. 10
E. 15
I think my answer is D. 10

triangle (half of parallelogram) has lengths of 3 and 5

for third side max is <(3+5) =<8
for third side min is >(5-3)= >2

To find the length of a diagonal in a parallelogram, we can use the property that the diagonals of a parallelogram bisect each other. This means that the diagonals divide each other into two equal parts.

In a parallelogram, the opposite sides are equal in length. Since the given parallelogram has side lengths of 3 and 5, we can assume that the other two sides are also 3 and 5, as they are opposite each other.

Now, let's draw the parallelogram and label the sides:

______
| |
|______|

Let's call the diagonal "d". According to the property, the diagonal divides the parallelogram into two congruent triangles, as shown below:

______
|\ |
| \ |
| \ t |
| \ |
|____\|

Since the sides of the parallelogram opposite each other are equal, the two triangles are congruent. Therefore, we can use the Pythagorean theorem to find the length of the diagonal:

d^2 = 3^2 + (5/2)^2

Simplifying, we have:

d^2 = 9 + 25/4
or
d^2 = (9*4 + 25)/4
or
d^2 = (36 + 25)/4
or
d^2 = 61/4

Taking the square root of both sides, we get:

d = √(61/4)

So, the length of the diagonal, "d," is the square root of 61 divided by 2 (√61/2).

Now, we can check if any of the options given are possible values for the length of the diagonal.