Question

Whats the answer & how do I solve it ?

Answer 1

Area of rectangle = 225/2 or 112.5

Explanation:

Given,

Consider a rectangle ABCD.

Let AC be a diagonal of rectangle of length = 15

In triangle ABC.

Sin 45° =height/hypotenuse {SinФ = height / hypotenuse}

Here, hypotenuse = diagonal of rectangle ( i.e AC = 15)

And height is AB

Therefore, sin 45° = AB/AC

or sin 45° = AB / 15

or 1/√2 = AB /15

AB = 15/√2

Similarly we can find Base (i.e BC) using cosine.

Cos 45° = Base/Hypotenuse

Cos 45° = BC / AC

or 1/√2 = BC/15

BC = 15/√2

Hence we got length of rectangle , AB= 15/√2

And width of rectangle , BC = 15/√2

Therefore, area of rectangle = Length × Width

Area of rectangle = 15/√2 × 15/√2 = 225/2

Hence, area of rectangle = 225/2 = 112.5