Parallelogram 65334

In a parallelogram, the sum of the lengths of the sides a+b = 234. The angle subtended by the sides a and b is 60°. The diagonal size against the given angle of 60° is u=162. Calculate the sides of the parallelogram, its perimeter, and its area.

Correct answer:

a = 181.6916
b = 52.3084
o = 468
S = 8230.7054

Step-by-step explanation:

a + b = 234 β = 60 ° = 60 u = 162 u^{2} = a^{2} + b^{2} - 2 \cdot a \cdot b \cdot cos β u^{2} = a^{2} + (234 - a)^{2} - 2 \cdot a \cdot (234 - a) \cdot 0.5 16 2^{2} = a^{2} + (234 - a)^{2} - 2 \cdot a \cdot (234 - a) \cdot 0.5 - 3 a^{2} + 702 a - 28512 = 0 3 a^{2} - 702 a + 28512 = 0 3 . . . prime number 702 = 2 \cdot 3^{3} \cdot 13 28512 = 2^{5} \cdot 3^{4} \cdot 11 GCD (3, 702, 28512) = 3 a^{2} - 234 a + 9504 = 0 p = 1; q = - 234; r = 9504 D = q^{2} - 4 p r = 23 4^{2} - 4 \cdot 1 \cdot 9504 = 16740 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{2 3 4 \pm 1 6 7 4 0}{2} = \frac{2 3 4 \pm 6 4 6 5}{2} a_{1, 2} = 117 \pm 64.691576 a_{1} = 181.691575959 a_{2} = 52.308424041 a = a_{1} = 181.6916

Our quadratic equation calculator calculates it.

b = 234 - a = 234 - 181.6916 = 52.3084

Try calculation via our triangle calculator.

o = 2 \cdot (a + b) = 2 \cdot (181.6916 + 52.3084) = 468

sin β = v : b v = b \cdot sin β = b \cdot sin 60 ° = 52.3084 \cdot sin 60 ° = 52.3084 \cdot 0.866025 = 45.30042 S = a \cdot v = 181.6916 \cdot 45.3004 = 8230.7054

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You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:

high school

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