The figure shows the 50 - foot side of a house and a proposed rectangular garden to be fences in on 3 sides.
The 3 sides, a, b, and x will be made of 40 feet of fencing.
Which of the following is an expression for a in terms of x?
A. 2x+40
B. 2x-40
C. 40-2x
D. 40-x+x
What is the area, in square feet, for the garden if 40 feet of fencing are used and x=15?

Option C 40-2 x

150 square feet

Step-by-step explanation:

Step 1 :

Given that the 3 sides, a,b, and x will be made of 40 feet of fencing,

we have a + b + x = 40

Since this is a rectangular garden , b= x

substituting b= x, we have a + x  + x = 40

=> a+2 x = 40

=> a= 40-2 x

Step 2 :

To find the area in square feet,

when x = 15, a = 40 -  2 * 15 = 40-30 = 10 feet

The length and breadth of the rectangular garden are therefore 5 and 10 feet respectively

Hence, the area of the garden = length  * breadth = 15 * 10 = 150 square feet

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!