Question

The diagonal of a rectangle is of length a. It splits each corner forming two angles with a ratio of 1:2. The area of the rectangle is: Select one: a. 1/2 a^2 b. 1/4 a^2 c. 2a^2 d.sqrt 2/2a^2 e. sqrt 3/4a^2 f/ sqrt 3/4a^2

Answer 1

Explanation:

Given

Length of diagonal is a

Diagonal divides the angle in 1:2

such that
`\theta +2\theta =90` (because angle between two sides is 90)

`3\theta =90`

`\theta =30^(\circ)`

width of rectangle is
`b=a\sin \theta =(a)/(2)`

Length of rectangle is
`L=a\cos 30=(√(3))/(2)a`

Area of rectangle
`A=L\cdot b`

`A=(√(3))/(2)a* (a)/(2)`

`A=(√(3))/(4)a^2`