Answer:
6/7 and 1 5/7
Step-by-step explanation:
Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
Using the rational root theorem, it is found that your friend is correct.
<h3>What is the rational root theorem?</h3>
- It is a theorem that states that for a polynomial with integer coefficients, with q being the factors of the leading coefficient and p being the factors of the constant, every <u>possible rational root</u> is the format
.
In this problem:
- The leading coefficient is 1, hence it's only factor is
, thus guaranteeing that every possible rational zero is an integer, which means that your friend is correct.
To learn more about the rational root theorem, you can take a look at brainly.com/question/10937559
Answer:
-1 and 5
Step-by-step explanation:
You would subtract 8 from both sides making it Z is greater than 4
