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

Answer:

$Length = 98$

Step-by-step 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:

$Length = AO * 2$

$Length = 49 * 2$

$Length = 98$