Question

A glass top of an office table is in the form of rectangle. The diagonal of the table have length 5x-11 and 2x+25

1.what is the value of x?
2.what us the length of the diagonal?​

Answer 1

1) The value of
`x` is 12.

2) The length of the diagonal is 49.

Explanation:

1) If the glass is a rectangle, then both diagonal must have the same length, that is, the following equation must be solved:

`5\cdot x - 11 = 2\cdot x + 25` (1)

We need some algebraic handling to determine the value of
`x`:

`5\cdot x - 11 = 2\cdot x + 25`

`5\cdot x - 2\cdot x = 25 +11`

`[5+(-2)] \cdot x = 36`

`3\cdot x = 36`

`x = 12`

The value of
`x` is 12.

2) If we know that
`x = 12`, then the length of the diagonal (
`d`) is:

`d = 2\cdot x + 25`

`d = 49`

The length of the diagonal is 49.