Question

1 point
#17: A rectangular shape has an area of 150 square units. The sides of the
rectangle measure (x + 3) and (x - 2). What is the value of x? (Type the final
answer as x=# without any space. Example: x=35 If there are two possible
values of x, write the final answer as follows: x=35 and x=36) *

Answer 1

Answer:

The only possible value of x is 12

Step-by-step explanation:

The rectangular shape has an area of 150 square units. The sides of the rectangle measures  (x + 3) and (x - 2).  The value of x can be computed below

area of a rectangle = length × breadth

area = 150 unit²

The sides are  (x + 3) and (x - 2)

Therefore,

(x + 3)(x - 2) = 150

x² -2x + 3x - 6 = 150

x²+ x - 6 = 150

x²+ x - 6 - 150 = 0

x²+ x - 156 = 0

(x - 12)(x + 13) = 0

Therefore,

x = 12 or x = -13

It cannot be - 13 because the sides cannot result to negative . We are left with only 12.

x = 12

The only possible value of x is 12

Answer 2

The value of x is 12

The dimensions of the rectangle are given as:

• Length = x + 3
• Width = x - 2

The area is given as:

• Area = 150

The area of a rectangle is:

$Area = Length \times Width$

So, we have:

$(x + 3)(x -2) = 150$

Expand

$x^2 + 3x - 2x - 6 = 150$

$x^2 + x - 6 = 150$

Subtract 150 from both sides

$x^2 + x - 156 = 0$

Factorize the above equation

$(x + 13)(x - 12) = 0$

Solve for x

$x = -13$ or $x =12$

The value of x cannot be negative.

So, the value of x is 12

Read more about areas at:

https://brainly.com/question/11202023