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
Answer:
Step-by-step explanation:
57.6
32+48 = 80
Four equivalent expressions are:
40+40 = 80
20+60 = 80
10+70 = 80
30+50 = 80
Hello!
The formula for the area of a circle is:
A = 
x r²
Answer:
2/3
Step-by-step explanation:
Divide 5/6 by 5/4
Find the Reciprocal of 5/4
5/6 times 4/5
5/3 time 2/5
10/15
2/3
