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04 Sep 2025, 22:47
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
100% (01:33) correct
0% (00:00) wrong based on 2 sessions
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The area of rectangular region ABCD is equal to the area of the isosceles trapezoid PQRS, with PS equal to QR. What is the length of segment QR?
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Updated on: 04 May 2026, 09:31
Originally posted by Sajjad1994 on 21 Sep 2025, 12:44.
Last edited by Sajjad1994 on 04 May 2026, 09:31, edited 3 times in total.
Last edited by Sajjad1994 on 04 May 2026, 09:31, edited 3 times in total.
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Explanation
As the area of the two diagrams is equal it means trapezoid area is 48. take average of two lengths of the trapezoid. \(\frac{9+15}{2}= 12\) so the height of trapezoid is = 4 (as 12*x=48 means x=4)
Calculate the Length of Segment QR
Since PQRS is an isosceles trapezoid, we can find the length of the side QR by creating a right angled triangle.
Draw a perpendicular line from R to the base PQ. The length of the segment XQ is half the difference between the two bases:
\(\frac{15 - 9}{2}= \frac{6}{2}= 3\)
Use the Pythagorean theorem \(a^2 + b^2 = c^2\) for the right triangle formed by the height h, the base segment XQ, and the side QR:
\(4^2 + 3^2 = QR^2\)
\(16 + 9 = QR^2\)
\(25 = QR^2\)
\(QR = 5\)
Answer: 5
As the area of the two diagrams is equal it means trapezoid area is 48. take average of two lengths of the trapezoid. \(\frac{9+15}{2}= 12\) so the height of trapezoid is = 4 (as 12*x=48 means x=4)
Calculate the Length of Segment QR
Since PQRS is an isosceles trapezoid, we can find the length of the side QR by creating a right angled triangle.
Draw a perpendicular line from R to the base PQ. The length of the segment XQ is half the difference between the two bases:
\(\frac{15 - 9}{2}= \frac{6}{2}= 3\)
Use the Pythagorean theorem \(a^2 + b^2 = c^2\) for the right triangle formed by the height h, the base segment XQ, and the side QR:
\(4^2 + 3^2 = QR^2\)
\(16 + 9 = QR^2\)
\(25 = QR^2\)
\(QR = 5\)
Answer: 5
02 May 2026, 18:01
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The answer should be 5 not 4
Sajjad1994
