Question

Find the value of the variable.

Answer 1

we are given that

both sides are equal

so, their length must be equal

$HK=\sqrt{(p-1)^2+(5-2)^2}$

$HK=\sqrt{(p-1)^2+9}$

now, we can find other side

$JK=\sqrt{(p-7)^2+(5-2)^2}$

$JK=\sqrt{(p-7)^2+9}$

now, we can set them equal

$HK=JK$

$\sqrt{(p-1)^2+9}=\sqrt{(p-7)^2+9}$

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