Answer:
The dimension of Length = L
The dimension of width = L
The dimension of Area = L²
Explanation:
A dimension is one of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.
L - length , W - width , A- Area
A= W × L (Formula for Area)
Given:
L= 4 + 3W ( length that is 4 more than 3 times its width)
Area = 480 inches
A= W × L
Sub. Given into Formula of Area
480= W (4 + 3W)
480= 4W + 3W²
3W² + 4W - 480= 0
a=3 b=4 c= -480
where W = unknown using the quadratic equation
W= -b ± √ (b² - 4ac) / 2a
W= -4 ± √ (4² - 4.3.-480)/ 2.3
W= -4 ± √ (16 + 5760)/ 6
W= -4 ± √ (5776)/ 6
W = (-4 ± 76)/6
W = (-4 + 76)/6 or (-4-76)/6
W = 72/6 or -80/6
W = 12 or - 13.6
We choose w=12 inches
Sub. W into L
L= 4 + 3W
L= 4 + 3×12
L= 40 inches
Area= W × L
= 40 inches × 12 inches
Area = 480 inches ²
Dimension wise
The dimension of Length = L
The dimension of width = L
The dimension of Area = L²
