Jorge has prepared his science project on a piece of poster board that has an area represented by the trinomial x2 + 5x – 50.

a) What are the dimensions of the board?
b) Write an expression for the perimeter of the board.
c) What is the actual perimeter of the board if x = 90 cm?

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help answer

To answer the questions, let's break down the problem step by step:

a) To find the dimensions of the board, we need to factor the trinomial x^2 + 5x - 50.

First, we can use factoring by splitting the middle term method. We need to find two numbers that multiply to give the constant term (-50) and add up to give the coefficient of the middle term (5).

The two numbers that satisfy this condition are 10 and -5.
So, let's rewrite the trinomial as (x + 10)(x - 5).

Now, the factors of the trinomial represent the dimensions of the board.
Therefore, the dimensions are:
Length = x + 10
Width = x - 5

b) Next, we need to write an expression for the perimeter of the board.

The perimeter of any geometric shape is calculated by adding up the lengths of all its sides. In this case, the perimeter of the board is the sum of all four sides.

The formula for the perimeter of a rectangle is:
Perimeter = 2(Length + Width)

Substituting the dimensions we found earlier, we get:
Perimeter = 2(x + 10 + x - 5)

Simplifying the expression, we have:
Perimeter = 2(2x + 5)

c) Finally, we need to find the actual perimeter of the board when x = 90 cm.

Substitute x = 90 into the expression we found above:
Perimeter = 2(2*90 + 5)

Calculating the expression, we have:
Perimeter = 2(180 + 5)
Perimeter = 2(185)
Perimeter = 370 cm

Therefore, the actual perimeter of the board when x = 90 cm is 370 cm.