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06 Apr 2020, 03:57
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
56% (02:35) correct
44%
(02:20)
wrong
based on 61
sessions
History
Date
Time
Result
Not Attempted Yet
We have a right triangle \(ABC\) with \(∠A = 90^o, AD = 6\) and \(CD = 8. AD\) and \(BC\) are perpendicular to each other. If \(x = AC\) and \(y = BD\), what is the value of \(xy\)?
4.6ps.png [ 8.7 KiB | Viewed 1763 times ]
A. \(40\)
B. \(42\)
C. \(45 \)
D. \(50\)
E. \(56\)
Attachment:
4.6ps.png [ 8.7 KiB | Viewed 1763 times ]
A. \(40\)
B. \(42\)
C. \(45 \)
D. \(50\)
E. \(56\)
06 Apr 2020, 06:52
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Using Pythagorus Theorem this problem can be solved
for triangle ADC: 36+64 = x^2 ; Hence x = 10
for traingle ADB: 36+y^2 = a^2 (Let AB = a)
For triangle ABC: 100+a^2 = (8+y)^2 = 64+y^2+16y
substitute a2 : 100+36+y^2 = 64+y^2+16y ; Hence y = 18/4
xy = 10*18/4 = 45
Hence the answer is C
for triangle ADC: 36+64 = x^2 ; Hence x = 10
for traingle ADB: 36+y^2 = a^2 (Let AB = a)
For triangle ABC: 100+a^2 = (8+y)^2 = 64+y^2+16y
substitute a2 : 100+36+y^2 = 64+y^2+16y ; Hence y = 18/4
xy = 10*18/4 = 45
Hence the answer is C
06 Apr 2020, 06:56
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Triangle ADC is right angle so by HP Theorem, AC = 10 = x
Since ABC, ABD and ADC all are right angle triangles all are similar by similarity properties
so
[AD][/BD] = [DC][/AD]
so 36 = 8y
and y = 4.5
so xy = 4.5 *10 = 45
Hence option C
Since ABC, ABD and ADC all are right angle triangles all are similar by similarity properties
so
[AD][/BD] = [DC][/AD]
so 36 = 8y
and y = 4.5
so xy = 4.5 *10 = 45
Hence option C
