Question

`HIJK` is a rectangle. If `HJ = 4x` and `IK = 7x-12`, what is the value of `x` and the length of each diagonal?

Answer 1

Since diagonals in a rectangle are always of equal length, we can write an equation that says that both dimensions are equal in length. See solution below.

Explanation:

`4x =7x - 12`

Solving for x:

`4x - 7x = -12`

`-3x = -12`

`x = 4`

Now, we can find the lengths of the diagonals by plugging in 4 for x.

`HJ = 4x`

`HJ = 4(4)`

`HJ = 16`

So, the diagonals measure 16 each.

Hopefully this helps.