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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.
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