Question

One of diagonals of a parallelogram is its altitude. What is the length of this altitude, if its perimeter is 50 cm, and the length of one side is 1 cm longer than the length of the other?

Answer 1

let AB be x,BC=x+1
perimeter=2AB+2BC
50=2x+2(x+1)
50=2x+2x+2
4x=48
x=12
AB=12
BC=AD=13
in ABD,ang.ABD=90
by Pythagoras theorem,
${(ad)}^{2} = {(ab)}^{2} + {(bd)}^{2} \\ {13}^{2} = {12}^{2} + {(bd)}^{2} \\ {(bd)}^{2} = 169 - 144$
$bd = \sqrt{25} \\ bd = 5$
therefore,altitude is 5cm