What is the length of a diagonal of a rectangle whose sides are 5cm and 12cm long?
A rectangle is a four-sided polygon with opposite pairs of sides congruent and all angles measure 90º.
Answer: The length of a diagonal of a rectangle whose sides are 5 cm and 12 cm long is 13 cm.
Let's find the length of the diagonal step by step.
Let ABCD be the rectangle.
In the above triangle ABCD, the diagonal AC divides the rectangle in two right angled triangles △ ABC and △ ADC.
Given In △ ABC,
AB = 12 cm, BC = 5 cm and AC = ?
By applying Pythagorean theorem of right triangle,
⇒ AC2 = AB2 + BC2
⇒ AC2 = (12 cm)2 + (5 cm)2
⇒ AC2 = 144 + 25
⇒ AC2 = 169
⇒ AC = √169
⇒ AC = 13 cm