Step-by-step answer:
Given:
A triangle
Perimeter = 60 cm
longest side = 4* shortest side (x)
Solution:
longest side = 4x
shortest side = x
third (intermediate side = 60 -x -4x = 60-5x
The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle. Hence
x + y > 4x
x + 60-5x > 4x
60 - 4x > 4x
8x < 60
x < 60/8 = 7.5, or
x < 7.5
Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.
Examine the options: both 7 and 5 are both less than 7.5 cm.
40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.
Now also examine cases where 4x is NOT the longest side, in which case we need
4x>=y
or
4x >= 60-5x
9x >=60
x >= 6.67
so x=5 will not qualify, because 4x will no longer be the longest side.
The only valid option is x=7 cm
The side lengths for x=7 and x=5 are, respectively,
(7, 25, 28)
5, 20, 35 (in which case, the longest side is no longer 4x=20, so eliminated)
The ones where I had to dance. For me, I am not a big fan of dancing and we had to do the la cha cha as our warm ups everyday. It was so weird. I think I rather do 5 push-ups, 10 sit-ups and jumping jacks for a warm up instead. :V
i dont have much time to go through all the work but i can tell you that since its a 90 degree angle, your equation would be 90=15x-2+7x+4. Once you get the value of X plug that into each of the equations. For example if your x value was 2 you would do 15(2)-2. Thats just an example.
Answer:
Angle A=Side MT
Angle M=Side AT
Angle T=Side AM
Step-by-step explanation: