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Q.

A rectangle has one of its vertical side lengths as 3 cm and a diagonal of length 5 cm. Determine the length of its adjacent side.

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a

4 cm

b

6 cm

c

8 cm

d

10 cm

answer is A.

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Detailed Solution

Given, a rectangle has one of its vertical side lengths as 3 cm and a diagonal of length 5 cm.
A rectangle is a parallelogram in which the adjacent sides are at right angles to each other.
Based on this definition, and the given side lengths, we have, the rectangle as follows,
Question Image

Question Image

So, we have to determine the side length of PO as it is the adjacent side of the vertical side ON of the rectangle.
Now, we can observe that the

Δ N O P

formed by the diagonal PN and the adjacent sides PO and ON of the rectangle MNOP is a right triangle.
So, by the Pythagoras theorem, we have,

(P O) 2 + (O N) 2 = (P N) 2 (P O) 2 + (3) 2 = (5) 2 (P O) 2 + 9 = 25 (P O) 2 = 25 − 9 (P O) 2 = 16 P O = 16 P O = 4

So, the length of the adjacent side is found to be 4 cm.
Hence, the correct option is (1).

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