Question

Consider parallelogram ABCD with diagonals that intersect at E. What value of x proves that the parallelogram is a rectangle if ED=7x+21 and AC=154?

a. 7
b. 8
c. 14
d. 19

Answer 1

I think it’s B I hope it helps

Answer 2

Therefore, the value of x that proves the parallelogram ABCD is a rectangle is x = 19. Option D

How to determine the value of x

To determine the value of x that proves the parallelogram ABCD is a rectangle, use the properties of diagonals in a rectangle.

In a rectangle, the diagonals are congruent and bisect each other. This means that if ABCD is a rectangle, then AE = CE and BE = DE.

Given that ED = 7x + 21, we can set it equal to BE:

ED = BE

7x + 21 = BE

We also know that AC = 154, which is the same as BE:

AC = BE

154 = BE

Setting the two expressions for BE equal to each other, we have:

7x + 21 = 154

Now, solve for x:

7x + 21 = 154

Subtract 21 from both sides:

7x = 154 - 21

7x = 133

Divide both sides by 7:

x = 133 / 7

x = 19

Therefore, the value of x that proves the parallelogram ABCD is a rectangle is x = 19.

The correct answer is (d) 19.