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Question
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
Options
5
3
`sqrt(34)`
4
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Solution
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is `underlinebb(sqrt(34))`.
Explanation:
The three vertices are: A = (0, 3), O = (0, 0), B = (5, 0)
We know that, the diagonals of a rectangle are of equal length,
Length of the diagonal AB = Distance between the points A and B
Distance formula: d2 = (x2 – x1)2 + (y2 – y1)2
According to the question,
We have,
x1 = 0, x2 = 5
y1 = 3, y2 = 0
d2 = (5 – 0)2 + (0 – 3)2
d = `sqrt((5 - 0)^2 + (0 - 3)^2`
d = `sqrt(25 + 9)`
= `sqrt(34)`
Distance between A(0, 3) and B(5, 0) is `sqrt(34)`
Therefore, the length of its diagonal is `sqrt(34)`
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