Question

11. The length of a rectangle is twice its width. If the length of its diagonal is 16√15 cm, find its area.​

Answer 1

Step-by-step explanation:

Consider a rectangle ABCD where AB = length,BC = breadth and AC = diagonal = 16root15

Also,all the interior angles in a rectangle are 90°.

Therefore,we can apply Pythagoras theorem in triangle ABC

=> AB^2+BC^2=AC^2

=> (2BC)^2 + BC^2 = (16 root 15)^2 [it is given that length is twice the width/breadth of rectangle,therefore AB=2BC]

=>4BC^2 + BC^2 = 3840

=> 5BC^2 = 3840

=> BC^2 = 3840/5

=> BC^2 = 768

=> BC = root768 = 16root3

therefore,AB = 2BC = 2×16root3 = 32root3

Area of rectangle = length × breadth

= AB×BC = 32root3×16root3

= 1536 cm^2 ans.