InterviewSolution
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InterviewSolution
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The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the value of p. |
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Answer» In `DeltaABC` `" "angleB= 90^(@)` `therefore" "AB^(2)+BC^(2)=AC^(2)` `rArr(p-4)^(2)+(3-7)^(2)+(p-7)^(2)+(3-3)^(2)=(7-4)^(2)+(3-7)^(2)` `rArr" "p^(2)-8p+16+p^(2)-14p+49+0=9` `rArr" "2p^(2)-22p+56=0` `rArr" "p^(2)-11p+28=0` `rArr" "p^(2)-7p-4p+28=0` `rArr" "p(p-7)-4(p-7)=0` `rArr" "(p-7)(p-4)=0` `rArr" "p-7=0 or p-4=0` `rArr" "p=7 or p=4` when p=7, then the points B and C coincide and so no triangle is formed. `therefore" "p ne7` Hence, `p` =4 |
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