ΔABC is a 45 - 45 - 90 triangle. The pattern of its sides is as follows:
Each leg = 1 unit (and both legs are that way, since the triangle is isosceles - so two sides are the same)
Hypotenuse = √2 units.
So if we know either leg, we multiply by √2 to get the hypotenuse. In reverse, we divide by √2 if we know the hypotenuse to get the measurement of a leg.
Our problem tells us that the hypotenuse AC is 10 units. We divide 10 by √2 to get the measurement of leg AB. Since it's a 45 -45 - 90 triangle, AB = BC.

to rationalize the radical

Thus, each leg is 5\sqrt{2} [/tex].
Answer:
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Answer:
see below
Step-by-step explanation:
3x^2 + 17x +10 =0
(3x+ ) ( x+ ) =0
We need to factor 10 = 2*5 or 1*10
They are positive since we have all positive terms
3*5 = 15+2 = 17
The 5 needs to multiply the 3 so it goes on the outside
(3x+ ) ( x+ 5 ) =0
That leaves the 2 on the inside
(3x+ 2 ) ( x+ 5 ) =0
Using the zero product property
3x+2 =0 x+5=0
3x = -2 x=-5
x = -2/3 x = -5
5 + 17a is the answer you are looking for