Bob wants to plant a 7 foot by 10 foot garden with a uniform border of petunias around the outside and still have 28 square feet

Answer:

The petunia border width is 1.5 feet.

Step-by-step explanation:

Let’s define x as the border width in feet,

Given,

The garden measurements are 7 feet by 10 feet,

Thus, the dimensions of the central area without the border are (7 - 2x) feet by (10 - 2x) feet.

Therefore, the central area = (7 - 2x)(10 - 2x)

According to the problem,

       ( Combine like terms )

 ( Middle term splitting )

By applying the zero product principle,

4x - 6 or x - 7 = 0

⇒ x = 1.5 or x = 7

Since the width cannot equal the garden dimensions,

It follows that the border width would be 1.5 feet.

Answer:

1.5 feet

Step-by-step explanation:

Bob is planning to create a garden that measures 7 feet by 10 feet.

Area = square feet

He intends to plant petunias in a uniform border around the garden while ensuring there is a leftover area of 28 square feet for tomatoes and roses in the center.

This requires factoring 28 so that both the length and width remain under 10 and 7 feet.

28 = 2 x 2 x 7

This indicates that the width can be 4 feet and 7 feet the length for the area meant for tomatoes.

Thus, we find that the garden reduces feet on every side, meaning the deduction on each side is feet.

Similarly, the width is also reduced by feet, resulting in a width reduction of 1.5 feet on each side.

Consequently, the petunia border should be 1.5 feet wide throughout.