Eleanor and Max used two rectangular wooden boards to make a set for the school play. One board was 6 feet long, and the other board was 5.5 feet long. The two boards had equal widths. The total area of the set was 60.375 square feet. What was the width?

Area = Length × Width
60 3/8 = (5 1/2 × w) + (6 × w) 60 3/8 = 11 1/2 + 2w 48 7/8 = 2w 24 7/16 = w
Width: 24 7/16

Answered by iloveonedirection | 2024-06-10

** The width is given by: **
w = 5 4 1 ​ ; By definition, the area of a rectangle is:
A = w ∗ l
Where,
w: width of the rectangle
l: length of the rectangle
The total area is given by:
A = A 1 + A 2
Where,
A1: rectangular wooden board 1
A2: rectangular wooden board 2
Substituting we have:
60 8 3 ​ = ( 6 ) ( w ) + ( 5 2 1 ​ ) ( w )
Rewriting we have:
8 483 ​ = ( 6 ) ( w ) + ( 2 11 ​ ) ( w )
[ 483 = 48w + 44w
483 = 92w ]
[ w = \frac{483}{92}
w = 5.25
]
w = 5 4 1 ​

Answered by carlosego | 2024-06-11

The width of the wooden boards is 5.25 feet, derived from the total area of 60.375 square feet and the lengths of the two boards. We calculated the area by using the lengths to form an equation and solving for width. This approach is based on the formula for the area of rectangles.
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Answered by iloveonedirection | 2024-09-30