Ms. Ahmed has a rectangular garden where she grows tomatoes. The length of her garden is represented by t + 4 and the width by 2t - 1.

Express the area of Ms. Ahmed's garden as a polynomial in standard form.

If the area of Ms. Ahmed's garden is 56 ft2, what are the dimensions of the garden?

area of the garden as a polynomial in standard form = 2t² + 7t - 4

The dimension will be 8 ft by 7 ft.

Step-by-step explanation:

The area of a rectangular shape is the product of the length and the width. Ms Ahmed rectangular garden with a length represented as t + 4 and width of 2t - 1, the area of the garden can be solved by multiplying both value.

Area of the garden = (t + 4) (2t - 1)

Area of the garden = 2t² - t + 8t - 4

Area of the garden = 2t² + 7t - 4

Expressing the area as a polynomial in standard form simply implies that the terms are express from the biggest exponent tot he lowest exponent. Therefore,

area of the garden as a polynomial in standard form = 2t² + 7t - 4

When the area is 56 ft².

2t² + 7t - 4 = 56

2t² + 7t - 4 - 56 = 0

2t² + 7t - 60 = 0

fin the numbers you can multiply to give you - 120 and add to give you 7. The numbers are 15 and - 8. Therefore,

2t² + 15t - 8t - 60 = 0

t (2t + 15) - 4 (2t + 15) = 0

(t - 4) (2t + 15) = 0

t = 4 or - 15/2

let use t = 4 as it is positive.

area = (t + 4) (2t - 1)

area = (4 + 4) (8 - 1)

area = 8 * 7 = 56 ft²

The dimension will be 8 ft by 7 ft.