Step-by-step explanation:
(B) L = 182.9 cm +- 0.1 cm
W = 152.4 cm +- 0.1 cm
(C)
Smallest dimensions possible:
L = 182.9 cm - 0.1 cm = 182.8 cm
W = 152.4 cm - 0.1 cm = 152.3 cm
A = (182.9 cm)(152.3 cm)
= 27840.44 cm^2
To find the uncertainty for the area ∆A, we use the formula
[tex] \frac{da}{a} = \frac{dl}{l} + \frac{dw}{w} [/tex]
where da = ∆A, dl = ∆L, dw = ∆W
[tex] \frac{da}{27840.44 {cm}^{2} } = \frac{0.1cm}{182.8cm} + \frac{0.1cm}{152.3cm} [/tex]
[tex] = 0.000547 + 0.000657[/tex]
[tex] = 0.001204[/tex]
Therefore
∆A = 0.001204 × 27840.44 cm^2
= 33.52 cm^2
Rounding off the numbers to their significant figures,
A = 27840 cm^2 +- 33 cm^2
(D)
For the largest possible area,
L = 183.0 cm
W = 152.5 cm
A = 27905.5 cn^2
[tex] \frac{da}{27907.5 {cm}^{2} } = \frac{0.1cm}{183.0cm} + \frac{0.1cm}{152.5cm} [/tex]
[tex] = 0.001202[/tex]
∆A = 0.001202 × 27907.5 cm^2
= 33.55 cm^2
Therefore, the largest possible area is
A = 27910 cm^2 +- 33 cm^2
