Question

1.ABCD is a rectangle.its diagonals meet at O.lif AO = 5x-1 and BO =

4x+9.find the length of the diagonals.(lengths in cm)​

Answer 1

`Length = 98`

Explanation:

Given

`AO = 5x - 1`

`BO = 4x + 9`

Required:

The length of the diagonal

Since AO and BO are diagonals that meets at O, we have:

`AO=BO`

This gives

`5x - 1 = 4x + 9`

Collect Like Terms

`5x - 4x = 1 + 9`

`x = 10`

Subsitute 10 for x in
`AO = 5x - 1`

`AO = 5 * 10 - 1`

`AO = 50 - 1`

`AO = 49`

The length of the diameter is:

`Length = AO * 2`

`Length = 49 * 2`

`Length = 98`