Question

The length of a rectangular piece of land is 15 m and its width is 8 m. Find the length of its diagonal. (If we draw a diagonal of a rectangle we get two right-angled triangles.)

Answer 1

Let ABCD be the given rectangle with length AB = 15 m and width BC = 8 m.


We have to find the length of diagonal AC.
We know that all the angles of a rectangle are of 90°
∴ $\angle$B = $\angle$C = $\angle$D = $\angle$A = 90°
∴ ∆ABC is right-angled at B.
By Pythagoras theorem,
(Hypotenuse)² = (side one)² + (side two)²
⇒ (AC)² = (AB)² + (BC)²
⇒ (AC)² = (15)² + (8)²
⇒ (AC)² = 225 + 64
⇒ (AC)² = 289
⇒ (AC)² = (17)²
⇒ AC = 17 m
∴ The length of the diagonal is 17 m.