The area if a rectrangular swimming pool can be represented by the trinomial expression 6xsqaured+5x-4. If x= 4m, what is the total area of the pool and what are it's dimensions?

Wherever there's an x, put in 4m and solve. 6(4m)^2+5(4m)-4=

Oh Thank you,

But them what are the dimensions?
How do i figure out that?

Our area of

6x^2 + 5x - 4 factors to
(3x+4)(2x-1)

so if x = 4

3x+4 = 16
2x-1 = 7

So the length is 16 and the width is 7

Note that 7(16) = 112 which is what you get if you follow Jen's substitution.

To find the total area of the pool, you need to substitute the value of x into the given trinomial expression and evaluate it.

Given: 6x^2 + 5x - 4

Step 1: Substitute x = 4m into the expression.
Area = 6(4m)^2 + 5(4m) - 4
= 6(16m^2) + 20m - 4
= 96m^2 + 20m - 4

Step 2: Simplify the expression.
Area = 96m^2 + 20m - 4

Now, to determine the dimensions of the pool, we can factorize the quadratic expression 96m^2 + 20m - 4.

Step 3: Factorize the quadratic expression.
Area = (8m - 1)(12m + 4)

From the factored form, we can see that the dimensions of the pool are (8m - 1) and (12m + 4). Now, plug in the value of x = 4m into these expressions to find the actual dimensions.

For length: Length = 8m - 1 = 8(4m) - 1 = 32m - 1
For width: Width = 12m + 4 = 12(4m) + 4 = 48m + 4

Therefore, the dimensions of the rectangular swimming pool, when x = 4m, are length = 32m - 1 and width = 48m + 4.