The figure shows an equilateral triangle with its sides as indicated. find the length of each side of the triangle .
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Supplementary angles measure 180°. Make an equation:
Subtract 28 to leave the variable in the parentheses alone:
Add the 2 x's together:
Your new equation is:
Divide both sides by 2 to leave the variable alone
The supplement measures 76°
Sum of all angles of a triangle is equal to 180°. Therefore,
A + B + C = 180
Given that, A = 4x, B = 3x + 1, C = 7x + 11.
Hence, we can set up an equation as following:
4x + 3x + 1 + 7x + 11 = 180
14x + 12 = 180 Combine the like terms.
14x + 12 -12 = 180 - 12 Subtract 12 from each sides.
14x = 168
Divide each sides by 14.
So, x= 12.
Now by plug in x=12 in the given expressions of A, B and C we can get the measure of eah angles of the triangle. Therefore,
A = 4x = 4(12) = 48
B= 3x + 1= 3(12) + 1 = 36 + 1 = 37
C= 7x + 11 = 7(12) + 11 = 84 + 11 =95
From the above result we can see that C is the largest angle and B is the smallest angle.
There is a relationship of a triangle which state that the largest side is opposite side of the largest angle and similarly smallest side is opposite side of the smallest angle.
Here AB is the opposite side of the largest angle C. So, AB is the largest side.
Similarly AC is the smallest side.
So, the order from shortest to longest is B: AC, BC, AB