Question

in figure ap is perpendicular on line l and and PR is greater than PQ show that ar is greater than aq

Answer 1

HERE,
IN RIGHT TRIANGLE APR

BY PYTHAGORAS THEOREM
${{ar}}^{2} = {pr}^{2} + {ap}^{2}$
therefore
${pr}^{2} = {ar}^{2} - {ap}^{2}$
---- 1
AGAIN SIMILARLY IN
TRIANGLE APQ
${pq}^{2} = {aq}^{2} - {ap}^{2}$
----2
But
PR>PQ {GIVEN}
Therefore
${pr}^{2} > {pq}^{2}$
------3
therefore
From 1 ,2 and 3
${ar}^{2} - {ap}^{2} > {aq}^{2} - {ap}^{2}$
therefore
${ar}^{2} > {aq}^{2}$
or
$ar > aq$
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