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CBSE Class 10 Answered

The ends of a diagonal of a square have coordinates (-2,p)and (p,2). Find P if the area of the square is 40 square units.
Asked by Gishin Rajan | 08 Feb, 2014, 04:38: PM
answered-by-expert Expert Answer
Length of diagonal= d
equals square root of left parenthesis minus 2 minus p right parenthesis squared plus left parenthesis p minus 2 right parenthesis squared end root
equals square root of left parenthesis 4 plus 4 p plus p squared right parenthesis plus left parenthesis p squared minus 4 p plus 4 right parenthesis end root
equals square root of 4 plus 4 p plus p squared plus p squared minus 4 p plus 4 end root
equals square root of 2 p squared plus 8 end root
Now, area of square = 40 sq. units
And, area of square = d squared over 2
Thus, we have
 
40 = fraction numerator 2 p squared plus 8 over denominator 2 end fraction
80 = 2(p2 + 4)
40 = p2 + 4
p2 = 36
p = plus-or-minus6
Answered by | 10 Feb, 2014, 10:13: AM

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