points d and e trisect the hypotenus bc of a right - angled traingle abc with angle = 90⁰. if ad = 7 and ae = 9 , find de ².
Answers
Answered by
2
Answer:
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Step-by-step explanation:
Since D and E are the points of trisection of BC therefore BD=DE=CE
Let BD=DE=CE=x.
Then BE=2x and BC=3x
In rt △ABD,
AD
2
=AB
2
+BD
2
=AB
2
+x
2
(i)
In rt △ABE,
AE
2
=AB
2
+BE
2
=AB
2
+4x
2
(ii)
In rt △ABC,
AC
2
=AB
2
+BC
2
=AB
2
+9x
2
(iii)
Now, 8AE
2
−3AC
2
−5AD
2
=8(AB
2
+4x
2
)−3(AB
2
+9x
2
)−5(AB
2
+x
2
)
=0
Therefore, 8AE
2
=3AC
2
+5AD
2
Answered by
1
Answer:
Since D and E are the points of trisection of BC therefore BD=DE=CE
Let BD=DE=CE=x.
Then BE=2x and BC=3x
In rt △ABD,
AD2=AB2+BD2=AB2+x2 (i)
In rt △ABE
AE2=AB2+BE2=AB2+4x2 (ii)
In rt △ABC,
AC2=AB2+BC2=AB2+9x2 (iii)
Now, 8AE2−3AC2−5AD2
=8(AB2+4x2)−3(AB2+9x2)−5(AB2+x2)
=0
Therefore, 8AE2=3AC2
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