A square is inscribed in a right angled triangle with legs p and q ,and has common right angle with the triagle. The diagonal of the square is given by
a)pq/p+2q
b)pq/2p+q
c)√2pq/p+q
d)2pq/p+q
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Answer:
C
Step-by-step explanation:
Let ABC be right angled triangle right angled at B
Let BDEF be the square inscribed.
As illustrated in the diagram(in the attachment below), it is clearly evident that triangles AFE and EDC are similar.
From properties of similar triangles, AF/ED = FE/DC
Thus, (q-x)/x = x/(p-x)
On solving above for x , we get x = pq/(p+q).
The diagonal of the square is x√2 = √2pq/p+q.
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