In the figure, `AD=17`, `AB=10`, `BC=15`. `/_ABC=/_BCD=90^(@)` seg `AE bot` side `CD` then find the length of `(i) AE` `(ii) DE` `(iii) DC`.

Explanation

In `square ABCE`,
`/_ABC=/_BCE=/_CEA=90^(@)`…….(Given)
`:./_EAB=90^(@)`…….(Remaining angle of a quadrilateral)
`:. Square ABCE` is rectangle.
`(i) :.AE=BC`……(Opposite sides of rectangle are equal)
`:.AE=15`
`(ii)` In `DeltaDEA`,
`/_DEA=90^(@)`
`:.` by Pythagoras theorem,
`AD^(2)=AE^(2)+ED^(2)`
`:.17^(2)=15^(2)+ED^(2)`
`:.ED^(2)=17^(2)-15^(2)`
`:.ED^(2)=289-225`
`:.ED^(2)=64`
`:.ED=8`
`(iii) CE=AB` .......(Opposite sides of rectangle are equal)
`:.CE=10`
`CD=CE+ED`.......`(C-E-D)`
`:.CD=10+8`
`:.CD=18`