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1.

In right angled `DeltaABC`, `BDbotAC`. If `AD=4`, `DC=9`, then find `BD`.

Answer» In `DeltaABC`, `ABC=90^(@)`…..(Given)
seg `Bdbot` hypotenuse `AC`.
`:.` by the theorem of geometric mean,
`BD^(2)=ADxxDC`
`:.BD^(2)=4xx9`
`:.BD^(2)=36`
`:.BD=6`……(Taking square roots of both the sides)
Discussion
2.

Find the side and perimeter of a square whose diagonal is `10cm`.

Answer» Let `square ABCD` be the given square.
`AC=10cm`
Let the side of the square be `x cm`
In `DeltaABC`,
`/_ABC=90^(@)`………(Angle of a square)
`:.` by Pythagoras theorem,
`AC^(2)=AB^(2)+BC^(2)`
`:.10^(2)=x^(2)+x^(2)`
`:.100=2x^(2)`
`{:( :.x^(2)=(100)/(2), :. x^(2)=50, :. x=5sqrt(2)):}`
`:.AB=5sqrt(2)cm`. `:.` side of square is `5sqrt(2)cm`.
Perimeter of a square `=4xx` side
`=4xx5sqrt(2)`
`=20sqrt(2)cm`
Discussion
3.

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`.

Answer» 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`
Discussion
4.

If `Delta ABC ` be an equilateral triangle and `AD _|_BC`, then `AD^(2)` =A. `(3)/(2) DC^(2)`B. `2DC^(2)`C. `3DC^(2)`D. `4DC^(2)`

Answer» Correct Answer - C
Discussion
5.

ABC is an isosceles triangle of which `AC=BC` and `AB^(2) = 2AC^(2)`. Then value of `/_C ` will be -A. `30^(@)`B. `90^(@)`C. `45^(@)`D. `60^(@)`

Answer» Correct Answer - B
Discussion
6.

A person at first travels 28m east from a certain place and then he travels `sqrt(57)`m south of it. The distance of the person from the starting point will beA. `(28+sqrt(57))m`B. 29 mC. `(28-sqrt(57))m`D. None of these

Answer» Correct Answer - b
Discussion