Question

In a rectangle ABCD, AC & BD intrest at O. If AO=2x+9 & BO=3x+5. find the measure of AC and BD.​

Answer 1

let ABCD is a rectangle

AC & BD Intersect at O

⇒ AC and BD are diagonals of a rectangle.

⇒ We know that diagonals of a rectangle are equal.

⇒ So, AC = BD

We can also write it as,

⇒ 2×OA=2×OB

2×(2x+9)=2×[3x+5)

4x+18 = 6x+10

4x=6x+10-18

4x =6x-8

4x-6x= - 8

-2x= -8

x =4

AO+OC =AC

2 (2×4+9) = 34

AC=34 cm

BD =2(3×4+5) = 34