question_answer

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

Answer:

Let ABCD be a rectangle such that AB = 40 cm and AC = 41 cm.

In right angled ∆ABC, right angled at B, by Pythagoras theorem, we have

\[B{{C}^{2}}=A{{C}^{2}}A{{B}^{2}}\]

\[={{41}^{2}}{{40}^{2}}\]

= (41 + 40) (41 ? 40)

= 81 × 1 = 81

BC = 81 = 9 cm,

Now, perimeter of rectangle

= 2(AB + BC)

= 2 (40 + 9) cm

= 2 × 49 cm = 98 cm 1