Verified answer

Problem:

The length of a rectangular garden is 7m longer than the width and its total area is 78 sq m. Which of the following equation bellow represents the given situation?

A) x + x + 7 = 78

B) x - x + 7 = 78

C) (x - 7)(x - 7) = 78

D) x(x + 7) = 78

Main Answer:

The x(x + 7) = 78 represents the given situation.

Additional Answer:

The value of x is x = 6, x = -13.

Step-by-step explanation:

Let,

x = the width of the rectangle

x + 7 = the length of the rectangle

Formula to get the area of a rectangle:

A = L * W

Solution:

Step 1: Multiply the x(x + 7) by applying the distributive property to it.

Step 2: Move the 78 to the left by subtracting from the both side.

Step 3: Get the factored form of x² + 7x - 78 by finding the pair integers that the product is -78 and the sum is 7. The pair integers that can be use there is -6 and 13.

Step 4: Make the (x - 6) equal to 0 and (x + 13) equal to 0.

Step 5: For (x - 6) = 0, add 6 to its both side. For (x + 13) = 0, subtract 13 to its both side.

The final answer is...

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