.ABCD is a rectangle in which segment AP and AQ are drawn such that angle QAD= angle PAB=30 degree. Find the length of (AP+AQ)
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The diagram shows Points P and Q.
As Sine of 30° is 1/2, we have BP/AP = 1/2
BP = AB / 2 => AP = √5 AB / 2 by using Pythagoras theorem.
Similarly AQ = √[AD² +DQ²] = √5 AD / 2
So AP + AQ = √5 (AB + AD) / 2
= √5 /4 of perimeter of rectangle.
As Sine of 30° is 1/2, we have BP/AP = 1/2
BP = AB / 2 => AP = √5 AB / 2 by using Pythagoras theorem.
Similarly AQ = √[AD² +DQ²] = √5 AD / 2
So AP + AQ = √5 (AB + AD) / 2
= √5 /4 of perimeter of rectangle.
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