If Diagonal of a Rectangle is 26 Cm and One Side is 24 Cm, Find the Other Side. - Mathematics

QUESTION

If diagonal of a rectangle is 26 cm and one side is 24 cm, find the other side.

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) =  √100 = 10 cm

Thus, the other side of the rectangle is 10 cm.