College

Find the lengths of the diagonals of rectangle QRST when \( QS = 20x - 5 \) and \( RT = 14x + 7 \).

A) 70
B) 99.7
C) 17.5
D) 35

Answer :

Final answer:

The lengths of diagonals QS and RT of rectangle QRST are found to be equal. By solving the given equations QS = 20x - 5 and RT = 14x + 7, we find x and thus the length of the diagonals, which is 35 units.

Explanation:

To find the lengths of the diagonals of rectangle QRST, we recall that in a rectangle, the diagonals are equal in length. Therefore, the length of diagonal QS must be equal to the length of diagonal RT. Given QS = 20x - 5 and RT = 14x + 7, we set them equal due to the properties of a rectangle.



So, 20x - 5 = 14x + 7. Solving for x, we get:



  • 20x - 14x = 7 + 5
  • 6x = 12
  • x = 2



Substituting x = 2 back into either QS or RT gives us:



  • QS = 20(2) - 5 = 40 - 5 = 35
  • RT = 14(2) + 7 = 28 + 7 = 35



The length of each diagonal is then 35 units. Therefore, the correct answer is D) 35.

ANSWER

D) 35

EXPLANATION

The rectangle is: