Question

Find the value of the variable.

Answer 1

we are given that

both sides are equal

so, their length must be equal

`HK=√((p-1)^2+(5-2)^2)`

`HK=√((p-1)^2+9)`

now, we can find other side

`JK=√((p-7)^2+(5-2)^2)`

`JK=√((p-7)^2+9)`

now, we can set them equal

`HK=JK`

`√((p-1)^2+9)=√((p-7)^2+9)`

now, we can take square both sides

`(p-1)^2+9=(p-7)^2+9`

now, we can solve for p

`(p-1)^2=(p-7)^2`

`p^2-2p+1=p^2-14p+49`

`-2p+1=-14p+49`

`12p=48`

`p=4`..............Answer