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प्रश्न
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
पर्याय
5
3
`sqrt(34)`
4
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उत्तर
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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Case Study -2
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Case Study -2
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It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
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