In △abc, point d∈ ac with ad: dc=4: 3, point e∈ bc so that be: ec=1: 5. if acde=5 in2, find abdc, aabd, and aabc.

In triangles with the same altitude, area is proportional to the base length. Triangles CDE and BDE both have the same altitude (the perpendicular distance from D to BC), so their areas are in the proportion BE:EC = 1:5. Since ACDE = 5 in², ABDE = 1 in². The area of BDC is the total of those:

... ABDC = 6 in²

Likewise, triangles ABD and CBD both have an altitude that is the perpendicular distance from B to AC. Then, ...

... AABD : ACBD = AD : CD = 4:3

Thus AABD = 4/3 × ACBD = 4/3 × 6 in²

... AABD = 8 in²

Of course, AABC is the sum of AABD and ABDC, so is ...

... AABC = 6 in² + 8 in²

... AABC = 14 in²

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.