The area of the enclosed space is given by the equation
(6+2x)² = 169
We can take the square root of both sides, since 169 is a perfect square:
√(6+2x)² = √169
6 + 2x = 13
Subtract 6 from each side:
6 + 2x - 6 = 13 - 6
2x = 7
Divide both sides by 2:
2x/2 = 7/2
x = 3.5
A.
Use PEMDAS
to get rid of the 3/4, divide both sides by 3/4 (.75) and 30 becomes 40
12x + 4 = 40
Subtract 4 from each side to cancel the - 4
12x = 36
Divide both sides by 12 to get rid of the 12
X = 3
Answer:
22 inches
Step-by-step explanation:
The longest stick that will fit in the box will be equal to the length of diagonal of the box.
Length of diagonal is given as:
![d = \sqrt{ {l}^{2} + {w}^{2} + {h}^{2} } \\ = \sqrt{ {20}^{2} + {6}^{2} + {6}^{2} } \\ = \sqrt{ 400 + 36 + 36} \\ = \sqrt{472} \\ = 21.725561 \\ = 22 \: inches](https://tex.z-dn.net/?f=d%20%3D%20%20%5Csqrt%7B%20%7Bl%7D%5E%7B2%7D%20%2B%20%20%7Bw%7D%5E%7B2%7D%20%2B%20%20%7Bh%7D%5E%7B2%7D%20%20%20%7D%20%20%5C%5C%20%20%20%3D%20%20%20%5Csqrt%7B%20%7B20%7D%5E%7B2%7D%20%20%2B%20%20%7B6%7D%5E%7B2%7D%20%20%2B%20%20%7B6%7D%5E%7B2%7D%20%7D%20%20%5C%5C%20%3D%20%20%20%5Csqrt%7B%20400%20%20%2B%20%2036%20%20%2B%20%2036%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B472%7D%20%20%5C%5C%20%20%3D%2021.725561%20%5C%5C%20%20%3D%2022%20%5C%3A%20inches)