can u anyone tell me how to solve this two question ?
http://s4.postimg.org/kg7fcmiyl/Untitled.jpg
PS: i don’t know the answers
thanks
19
Let C=weight of one crate
Let B=weight of one barrel
Let n=# of barrels
Given 6n = #crates
Given B = 9C
Total weight = total wt crates + total wt barrels
Total weight = 6nC + nB
Total weight = 6nC + n9C
Total weight = 6nC + 9nC
Total weight = 15nC
Given 1200=total wt barrels = 9nC
solve nC= (1200/9) = (400/3)
Total weight = 15nC = 15 (400/3) = 2000 kilos
20 We know the measure of angle G because those 4 middle angles must total 360 degrees.
Therefore angle G = 360- 90 - 60 - 90 (90 from the squares and 60 from the equilat triangle).
G = 120
Now we know the measure of the angles in the bottom triangle…360 - 120 = 60; 60/2 = 30
Use Law of Sines:
AF/sin 120 = 6/sin 30
Answer is 6 (sqrt 3)
Slightly different solution to #20 (no trig required):
Drop an altitude from G to AF; call the midpoint/foot of the altitude M. Then GMA and GMF are 30-60-90 right triangles with hypotenuse 6, so we have GM = 3 and MA = MF = 3 sqrt(3), so AF = 6 sqrt(3).
PS: Interesting Chinese characters in the background…
I can explain them in a different way as well!
So 1 barrel and 6 crates are on the truck… And 1 barrel is 9x a crate.
What I did was I made the barrel = 1kg and the crates = .11 (1/9) each because each is 11% of the barrel. So .11 times 6 (because there are 6 crates) = .66
So the ratio found here is .66:1… Then we find out that all the barrels = 1,200 kg.
So, using the ratio of .66:1, we can find that 1,200 (.66) = 800.
So the weight of all the crates = 800 kg and the weight of all the barrels = 1,200 kg.
800 + 1200 = 2,000 kg.
For number 2:
By reading the problem, you can find out that every side is 6 except for the side on the bottom.
The isoceles (however you spell that lol) triangle at the bottom has sides AG (6) and AF (6).
The first three things I ruled out after this were A, C, and E because they do not follow the triangle side theorum (The theorum that says any 2 sides of a triangle must be bigger than the third and not equal either). AG + AF = 12, and because 12, 12 root 3 and 12 root 2 are equal or greater than 12, they cannot be the answers.
So we are left with B and D (THE ABOVE STEP WAS NOT NECESSARY… BUT THAT CAN BE HELPFUL IF YOU ARE EVER UNSURE… AND IT EASILY GIVES YOU A 50% CHANCE VERSUS A 0% CHANCE!)
Anyways, if you make a line between G and AF, this gives you the height of the triangle. But we aren’t looking for the height! Anyways, if you make a line there, you can also make a 90’ angle. So basically, I split triangle GFA into 2, and created a 90’ angle by splitting the two sides.
Angle G has been split into 2 and measures 60 degrees, while F measures 30 degrees. Now that we know this triangle is a 30-60-90 degree triangle, we can find half of the side of AF:
GF = 6 (hypotenuse), G to the middle of AF = 3 (smallest side is always half of hypotenuse) and the midpoint of AF to F = 3 root 3.
So we found that half of AF = 3 root 3… So the full length is 6 root 3.
thaanks a lot everyone u really helped
@Nigoni Well, more precisely, the sum of the lengths of any two sides of a triangle is strictly larger than the length of the third. Btw, it is spelled “theorem.”
But yes, I didn’t notice until you pointed out that A, C, and E are instantly out - good catch. Between B and D, one could easily guess it is D) 6 sqrt(3), since sqrt(2) doesn’t come up often when dealing with 30-60-90 triangles with integer side lengths…
Yeah, that was what I meant to say (not the best at explaining things 100% in English yet lol!). And thanks for correcting my spelling.
Good luck Omar!