Question

In rectangle PQRS, PR = 18x – 28 and QS = x + 380. Find the value of x and the length of each diagonal.

Answer 1

x = 24, PR = 404, QS = 404

Explanation:

PR and QS are both diagonals of the rectangle. The diagonals of a rectangle bisect each other and are of equal length. Thus, we can say:

PR = QS

18x - 28 = x + 380

Solving for x, we get:

18x - x = 380 + 28

17x = 408

x = 408/17

x = 24

Thus, PR = 18(24) - 28 = 404 and QS = 24 + 380 = 404

Third choice is right.