Question

The perimeter of the shape below is 11z² +7z + 1. Find the length of the missing side.

2x - 3
O-4x²2x² + 12
○ 4x² +5
O-4x² - 2x - 7
42²-8
7x² + 3x + 2
2x - 3

Answer 1

The length of the missing side is 4x² +5. therefore, option b. 4x² +5 is correct.

Perimeter formula:

The perimeter of a shape is the sum of the lengths of all its sides.

Perimeter = side 1 + side 2 + bottom + missing top side

Substituting given values:

We are given the values of two sides and the bottom:

Perimeter =
`(2x - 3) + (2x - 3) + (7x ^ 2 + 3x + 2)` + missing top side

Rearranging and simplifying:

Combine like terms:

Perimeter =
`11x ^ 2 + 7x + 1 +` missing top side

Isolating the missing side:

To find the missing top side, subtract all known sides from the perimeter:

missing top side = Perimeter - (side 1 + side 2 + bottom)

missing top side =
`(11x ^ 2 + 7x + 1) - [(2x - 3) + (2x - 3) + (7x ^ 2 + 3x + 2)]`

missing top side =
`(11x ^ 2 + 7x + 1) - (7x ^ 2 + 7x - 6)`

missing top side =
`4x^2 +5`

Therefore, option b. 4x² +5 is correct.