Question

# $$ABCD$$ is a rectangle. Its diagonals meet at $$O$$.Find '$$x$$', if $$OA=2x+4$$ and $$OD=3x+1$$.

A
2
B
3
C
3
D
2

Solution

## The correct option is B $$3$$$$\Rightarrow$$  In the given figure ABCD is a rectangle.$$\Rightarrow$$  $$OA=2x+4$$ and $$OD=3x+1$$               [Given]$$\Rightarrow$$  AC and BD are diagonals of a rectangle.$$\Rightarrow$$  We know that diagonals of a rectangle are equal.$$\Rightarrow$$  So, AC = BDWe can also write it as,$$\Rightarrow$$  $$2\times OA=2\times OD$$$$\Rightarrow$$  $$2 \times (2x+4)$$ $$= 2\times (3x+1)$$$$\Rightarrow$$  $$2x+4=3x+1$$$$\therefore$$   $$x=3$$Mathematics

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