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:
CD is perpendicular to AB
If any radius or diameter is perpendicular to any chord of a circle, then it bisects that chord.
Mean, AB= BE = 12
So, AB = 2(BE)
2(12)= 24
so your answer will be 24
hope it helps..
have a great day!!
The measure of angle 1 is 60* since it is 1/6 of 360*.
Answer:
2x⁴ + 4x³ + x² + 8x - 6
Step-by-step explanation:
(2x² + 4x - 3)(x² + 2)
2(x² + 2) · x² + 4x(x² + 2) - 3(x² + 2)
2x⁴ + 4x² + 4x(x² + 2) - 3(x² + 2)
2x⁴ + 4x² + 4x³ + 8x - 3x² - 6
2x⁴ + x² + 4x³ + 8x - 6
2x⁴ + 4x³ + x² + 8x - 6
