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26 Nov 2022, 08:45
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
80% (02:19) correct
20%
(02:05)
wrong
based on 20
sessions
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Date
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Not Attempted Yet
In square PRSU shown, Q and T are midpoints of sides PR and SU, respectively, and the length of QS is √5. What is the area of quadrilateral PQST?
A. 1
B. 2
C. 3
D. 4
E. 5
Attachment:
2022-11-25_18-37-34.png [ 25.78 KiB | Viewed 1846 times ]
26 Nov 2022, 08:55
Kudos
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Let PR = 2x, therefore QR=x
Now QRS is a right angle triangle
x^2 + (2x) ^2 = 5
x^2 + 4x^2 = 5
5x^2= 5
x=1.
Area of triangle QRS = (1/2)*1*2=1.
Area of triangle PUT = 1. (triangle QRS is congruent to PUT).
Area of square= 2^2 =4
Area of quadrilateral PQST = 4-1-1= 2.
Hence B is the correct choice.
Posted from my mobile device
Now QRS is a right angle triangle
x^2 + (2x) ^2 = 5
x^2 + 4x^2 = 5
5x^2= 5
x=1.
Area of triangle QRS = (1/2)*1*2=1.
Area of triangle PUT = 1. (triangle QRS is congruent to PUT).
Area of square= 2^2 =4
Area of quadrilateral PQST = 4-1-1= 2.
Hence B is the correct choice.
Posted from my mobile device
