Answer:
-6
Step-by-step explanation:
= -3 × -3
-3 × -3 = 9
7 × -3 =-21
9 - 21 +6 = -6
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
First you need to find the surface area of the wall that was painted, and then add the additional area in the hallway that was painted.
The wall that was painted was 9 feet by 10 feet, or 90 square feet. 90 square feet plus the additional 46 square feet in the hallway is 136 square feet, which is the total area that the paint covered.
Therefore the solution is 136 square feet.
One ounce is one-sixteenth of a pound since there is 16 ounces in a pound.
