The sides of the triangle are given as 1, x, and x².
The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.
Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.
Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.
Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.
Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.
4/5 x 1 1/6
<span>= 4/5 x (6 x 1 + 1)/6 </span>
<span>= 4/5 x 7/6 </span>
<span>= (4 x 7)/(5 x 6) </span>
<span>= 28/30 </span>
<span>= (28 ÷ 2)/(30 ÷ 2) </span>
<span>= 14/15</span>
I ain’t never seen two pretty best friends
Just divide 300 by 4 since 25% is 1/4
300/4 = 75
D. 75
Hope this helps!
