find the height of the lamp post.ĐĐž \ In a rhombus ABCD the diag

1.	find the height of the lamp post.ĐĐž \ In a rhombus ABCD the diagonals bisect at 0. Prove that AC, BD" 4 AB2
Answer» Let ABCD is rhombus AC and BD are diagonals we know that, AB=BC=CD=AD If O is centre, AO = OC = AC/2 BO = OD = BD/2 In triangle AOB, AB² = AO² + BO² => AB² = (AC/2)² + (BD/2)² => AB² = AC²/4 + BD²/4 => AB² = AC²+BD²/4 => 4AB² = AC² + BD² Hence proved

find the height of the lamp post.ĐĐž \ In a rhombus ABCD the diagonals bisect at 0. Prove that AC, BD" 4 AB2

Answer»

Let ABCD is rhombus

AC and BD are diagonals

we know that,

AB=BC=CD=AD

If O is centre,

AO = OC = AC/2

BO = OD = BD/2

In triangle AOB,

AB² = AO² + BO²

=> AB² = (AC/2)² + (BD/2)²

=> AB² = AC²/4 + BD²/4

=> AB² = AC²+BD²/4

=> 4AB² = AC² + BD²

Hence proved