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) *

The value of x is 12

The dimensions of the rectangle are given as:

The area is given as:

The area of a rectangle is:

So, we have:

Expand

Subtract 150 from both sides

Factorize the above equation

Solve for x

or

The value of x cannot be negative.

So, the value of x is 12

Read more about areas at:

link

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

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240