MATHEMATICS MIDDLE SCHOOL

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) *

Answers

Answer 1
Answer:

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 * 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:

brainly.com/question/11202023
Answer 2
Answer:

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

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