A rectangle has length 24 cm and diagonals of length 25 cm each. The area of the rectangle (in cm2):
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 168
The corners of a rectangle are right angles, so a diagonal is the hypotenuse of a right triangle whose other two sides are the length and the breadth. Pythagoras’ theorem gives the breadth, and then area = length × breadth.
Breadth, the third side of the right triangle: \(\sqrt{25^2-24^2}=\sqrt{625-576}=\sqrt{49}=7\,\mathrm{cm}\)
Area: \(24\times7=168\) cm2