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

Answer 1

Answer:

1) The value of $x$ is 12.

2) The length of the diagonal is 49.

Step-by-step 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.