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Question
If diagonal of a rectangle is 26 cm and one side is 24 cm, find the other side.
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Solution
Suppose ABCD is a rectangle.
Here, segment AC is a diagonal and segment AD is one side of the rectangle ABCD.
l(AC) = 26 cm and l(AD) = 24 cm.
In right ∆ACD,
l(AC)2 = l(AD)2 + l(CD)2 ...(Pythagoras theorem)
⇒ l(CD)2 = l(AC)2 − l(AD)2
⇒ l(CD)2 = (26)2 − (24)2
⇒ l(CD)2 = 676 − 576 = 100
⇒ l(CD) = `sqrt(100)` = 10 cm
Thus, the other side of the rectangle is 10 cm.
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