ABCD is a square. X is the mid-point of AB. Y is a point on BC such that BY = $$\frac13$$​ BC. If the area of BXY is equal to 300 cm², find length of diagonal AC.

Correct option is A

Given:
X is midpoint of AB.

BY = $$\frac13$$​BC 

Solution:

Side of the square are equal. and angle are 90 degree

AX = BX (midpoint X) 

Area of $$\triangle BXY = \frac12 \times BX \times BY$$ 

BX = $$\frac 12 AB$$ 

So, 

300 = $$\frac12 \times \frac{AB}2\times \frac{BC}{3}$$  (AB = BC) 

​$$\implies AB = 60 cm$$ 

Thus, AC(diagonal) = $$\sqrt{AB^2 + BC^2} = \sqrt{60^2 + 60^2} = 60\sqrt{2} \ cm$$​​

​