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(a+b)^3 = a^3+b^3+3ab(a+b)
(a+b)^3 = (-1)^3
Diagonal of the square (d):
d = a · √2 = a · 1.414 ( a is a length of a side of the square )
a = 9 : 1.414 = 6.365 inches
Total length:
4 · a + 2 · d = 4 · 6.365 + 2 · 9 = 25.46 + 18 = 43.46 ≈ 43.5 inches.
Answer: A ) 43.5
The answer is: Two possible solutions which are (0.53, 37.19)
Explanation:
Given:
A = 30°
<span>a = 20 </span>
<span>b = 16 </span>
Now use the law of Cosines:
a² = b² + c² - 2bc*cos(A)
Plug in the values:
20² = 16² + c² - (2*(16)*c*cos(30))
<span>400 = 256 + c² - 32c(0.866) </span>
<span>400 = 256 + c² - 27.71c </span>
<span>c² - 27.71c = 400 - 256 </span>
<span>c² - 27.71c = 144 </span>
<span>c² - 27.71c + 191.96 = 144 + 191.96 </span>
<span>(c - 18.86)² = 335.96 </span>
<span>c - 18.86 = √336.95 </span>
<span>c - 18.86 = ± 18.33 </span>
<span>c = 18.86 ± 18.33 </span>
<span>If c = 18.86 + 18.33, then </span><span>c = 37.19 </span>
<span>If c = 18.86 - 18.33, then </span><span>c = 0.53 </span>
<span>c = (0.53, 37.19) Two solutions!</span>
