Answer:
Width = 1.77ft
Length = 6.98ft
See explanation below
Explanation:
We can tell from the question, we are to find the the two possible lengths of a rectangle given the diagonal and the area. This question is not complete as it didn't indicate the area.
I would show you how to calculate the two possible lengths of a rectangle given the diagonal and the area.
Mary crocheted a rectangular blanket whose diagonal measures approximately 7.21 feet and area measures 12.4ft² approximately. What are the most likely length and width measurements of the blanket ?
The blanket is a rectangle
Diagonal = 7.21feet
Area measures = 12.4ft²
Formula for relating the diagonals to the length and width:
Diagonal² = length ² + width²
7.21² = l² + w²
l² = 7.21²-w²
l = √(7.21²-w²) ...equation 1
Area of a rectangle = length × breadth
12.4 = l × w ...equation 2
Substitute equation 1 in equation 2
12.4 = √(7.21²-w²) × w
12.4 = √(51.9841-w²) × w
Square both sides
12.4² = (51.9841-w²) × w²
153.76 = 51.9841w² - w⁴
w⁴ - 51.9841w² + 153.76 = 0
Using the almighty formula
Find attached the solution to the equation
From the solution width = 1.77ft or 6.98ft
Since width is shorter than length
Width = 1.77ft
Length = 6.98ft
The most likely length and width measurements of the blanket are 1.77ft and 6.98ft respectively.