The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal, it is obtained by Pythagoras theorem.
Step-by-step explanation:
The given are,
From ΔABC,
AB= 6
BC= 10
AC = x
From ΔDEC,
CD= 28
DE= 21
CE = y
Step:1
Pythagoras theorem from ΔABC,
[tex]BC^{2}=AB^{2} + AC^{2}[/tex]...............(1)
Substitute the values,
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]AC^{2}[/tex]
100 = 36 + [tex]AC^{2}[/tex]
[tex]AC^{2}[/tex] = 100 - 36
= 64
AC = [tex]\sqrt{64}[/tex]
AC = 8
AC = x = 8
Step:2
Pythagoras theorem for ΔDEC,
[tex]CE^{2} = CD^{2} + DE^{2}[/tex]................(2)
From the values,
[tex]CE^{2}[/tex] = [tex]28^{2}[/tex] + [tex]21^{2}[/tex]
[tex]CE^{2}[/tex] = 784 + 441
= 1225
CE = [tex]\sqrt{1225}[/tex]
CE = 35
CE = y = 35
Result:
The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal.
