Answer:
Step-by-step explanation:
Since ABC is an equilateral triangle, thus AB=BC=AC=x, therefore
The perimeter of ΔABC=36
⇒AB+BC+AC=36
⇒x+x+x=36
⇒3x=36
⇒x=12
Thus, AB=BC=AC=12.
Now, Since ΔADC is isosceles triangle, therefore AD=DC=y.
Perimeter of ΔADC=40
⇒AD+DC+CA=40
⇒x+y+y=40
⇒12+2y=40
⇒2y=28
⇒y=14
Therefore, AD=DC=14
Thus, Length of sides of ΔABC are AB=BC=AC=12 and Length of sides of ΔADC are AD=DC=14.
Answer:
4033
Step-by-step explanation:
An easy way to solve this problem is to notice the numerator, 2017^4-2016^4 resembles the special product a^2 - b^2. In this case, 2017^4 is a^2 and 2016^4 is b^2. We can set up equations to solve for a and b:
a^2 = 2017^4
a = 2017^2
b^2 = 2016^4
b = 2016^2
Now, the special product a^2 - b^2 factors to (a + b)(a - b), so we can substitute that for the numerator:
<h3>We can notice that both the numerator and denominator contain 2017^2 + 2016^2, so we can divide by which is just one, and will simplify the fraction to just:
2017^2 - 2016^2
This again is just the special product a^2 - b^2, but in this case a is 2017 and b is 2016. Using this we can factor it:
(2017 + 2016)(2017 - 2016)
And, without using a calculator, this is easy to simplify:
(4033)(1)
4033