The midsegment is half the length of the base. So the base = 2*4 = 8 in.
Since it is an isosceles triangle, the other two sides are equal in length.
Perimeter = sum of two equal sides + base = 20 in.
2x equal side + 8 = 20
equal side = 12/2 = 6
Each of the equal sides = 6"
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Answer:

Step-by-step explanation:
First of all, subtract 12 from both sides of the equation to put it into standard form:
3x² +8x -12 = 0
Then identify the a, b, c of this form:
ax² +bx +c = 0
You see that a=3, b=8, c=-12.
Now use those values in the quadratic formula for the solutions:

Answer and Step-by-step explanation: The described right triangle is in the attachment.
As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:
AC² = AB² + BC²




AB = 5.4
Then, right triangle ABC measures:
AB = 5.4cm
BC = 4.5cm
AC = 7cm
Given: sin theta = 2/5. This tells us that the lengths of the opp side and the hyp are 2 and 5 respectively. The adj side is found using the Pyth. Thm.: 5^2-2^2= 25-4 = 21, so that the adj side is sqrt(21).
The double angle formula for the sine is sin 2theta = 2 sin theta *cos theta.
In this particular problem, the sine of 2theta is 2*(2/5)*[sqrt(21) / 5], or:
(4/25)*sqrt(21).