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.
Answer: 54:150
Step-by-step explanation:
The ratio of bass to catfish in a pond can be written as 54:150
Answer:
D.) 9*pi >27
Step-by-step explanation:
9*pi = 28.2743338823...
28.2743338823... > 27
D.) 9*pi > 27 = True
Regards!
V = length×width ×height
V = 9 × 2 × 3
V = 54 units cubed
On 6/25 divide 6 by 25=.24 and 2 3/4= 2.75 you have 2 and then 3/4=.75
