HELP WITH THIS!

Part 1: Only these two: x(x + 5) = 24  and  (x + 5)(x) = 24

 

Part 2:

Area = Length x Width

Area =x(x + 5) =24

        =x^2 + 5x - 24 = 0, solve for x

Solve for x:
x^2 + 5 x - 24 = 0

The left hand side factors into a product with two terms:
(x - 3) (x + 8) = 0

Split into two equations:
x - 3 = 0 or x + 8 = 0

Add 3 to both sides:
x = 3 or x + 8 = 0

Subtract 8 from both sides:
Answer: |x = 3                  or                   x = -8

 

So the width =3 inches, and the length:

3 + 5 =8 inches.

Area = l x w     and area = 24 

Let length = x    then width = x+5

area = l * w     Substitue the values we have above

24 = x (x+5)       or   (x+5)x

 

Solve for x      24 = x(x+5)

24 = x^2 + 5x

0= x^2 + 5x -24

(x-3)(x+8) = 0         so x = 3  or -8 (throw this one out....you can't have length of -8)

                              so l= 3     w = l+5 = 8           8 x 3 = 24 in^2      CHECK!

Part 1:

x(x + 5) = 24

Part 2:

x(x + 5) = 24

1st way: By trial and error(not recommended because in exam you will only get the marks for the answer but not the steps)

x = 3, (x+5) = 8

Therefore width = 3 inches and length = 8 inches.

x(x + 5) = 24

2nd way: By factorization(highly recommended if you are really good at factorization)

x^2 + 5x = 24

x^2 + 5x - 24 = 0

(x - 3)(x + 8) = 0

x = 3 or x = -8(rejected)

Therefore x = 3 and x + 5 = 8

Therefore width = 3 inches and length = 8 inches.

3rd way: By quadratic equation

x(x + 5) = 24

x^2 + 5x - 24 = 0

x = (- 5 +- sqrt(5^2 - 4*1*(-24)))/(2*1)

x = (-5 +- 8)/(2*1)

x = 3 or -8(rejected)

Therefore width = 3 inches and length = 8 inches