Answer: The ratios APBQ : APBC=4:21 and AAQP : AABC= 3:28
Explanation:
Here, ABC is a triangle where, P and Q are the midpoints of the edges AC and AB respectively,
Now, according to the question ,AP:PC=1:3 let AP=x and PC=3x where x is any real number. Thus, AC=AP+AC= x+3x= 4x
Similarly, AQ:QB=3:4 let AQ=3y and QB=4y where y is also any real number. Thus, AB=AQ+QB=3y+4y=7y
Since,
And,
Answer:
Dimensions: 0.4 by 3.2 by 1.2
Step-by-step explanation:
I'm assuming here that we are cutting out squares out of each of the metal's corners:
Let x = the length of each cut-out square,
Each base (of the desired net square folded) is 4-2x, and 2-2x respectively,
Volume = x(4-2x)(2-2x)
= 4x^3 - 12x + 8x
Now we take the derivative:
We equate to 0 (0 for max volume), and solve using the quadratic formula:
So we approximate the side lengths to be 1.6 and 0.4 respectively. But when we plug in 1.6 for x, we get the volume as negative. Therefore x has to be 0.4.
Side lengths: 0.4, 4-2(0.4) => 3.2, 2-2(0.4) => 1.2