The length of the base of the isosceles triangle is: 27 units long.
<h3>What is an isosceles Triangle?</h3>
A triangle with two equal legs and a base is called an isosceles triangle.
Thus:
Let x represent the length of each of the equal legs of the isosceles triangle.
Therefore:
The length of the base = 1 1/2(x) = 1.5x units
Perimeter = 63
Therefore:
x + x + 1.5x = 63
3.5x = 63
x = 63/3.5
x = 18
The length of the base = 1.5x units
Plug in the value of x
The length of the base = 1.5(18) = 27 units
Therefore, the length of the base of the isosceles triangle is: 27 units long.
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The true statement about the directrix is that each directrix of this ellipse is 31.25 units from the center on the major axis.
<h3>How to determine the distance of the directrix?</h3>
The equation of the ellipse is given as:

The above means that:
a^2 = 625
a = 25
b^2 = 225
b = 15
Calculate c using:
c^2 = a^2 - b^2
This gives
c^2 = 625 - 225
Evaluate the difference
c^2 = 400
Evaluate the square root
c = 20
The equation of the directrix is
x - x₀ = ± a²/c
So, we have:
x - x₀ = ± 625/20
Evaluate the quotient
x - x₀ = ± 31.25
This means that, each directrix is 31.25 units from the center on the major axis.
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Answer:
Explanation:
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