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Question

$$ABCD$$ is a rectangle. Its diagonals meet at $$O$$.
Find '$$x$$', if $$OA=2x+4$$ and $$OD=3x+1$$.
508296.jpg


A
2
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B
3
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C
3
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D
2
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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 = BD
We 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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