Answer:
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.
