SOLUTION: Hi. Could you explain how to do the following problems using the Pythagorean Theorem to find x? 1. Triangle with legs of 4a and 3a, find x. 2. Equilateral triangle, with

Algebra ->  Absolute-value -> SOLUTION: Hi. Could you explain how to do the following problems using the Pythagorean Theorem to find x? 1. Triangle with legs of 4a and 3a, find x. 2. Equilateral triangle, with      Log On


   

Question 34951: Hi. Could you explain how to do the following problems using the Pythagorean Theorem to find x?
1. Triangle with legs of 4a and 3a, find x.
2. Equilateral triangle, with x running down the center.
Thanks for any help you can give.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Hi. Could you explain how to do the following problems using the Pythagorean Theorem to find x?
1. Triangle with legs of 4a and 3a, find x.
HYPOTENUSE^2=SQUARE OF 0NE LEG+SQUARE OF OTHER LEG
=(4A)^2+(3A)^2=16A^2+9A^2=25A^2
HYPOTENUSE=SQRT(25A^2)=5A
2. Equilateral triangle, with x running down the center.
Thanks for any help you can give.
LET ABC BE THE EQUILATERAL TRIANGLE WITH EACH SIDE OF a.LET AD BE THE ALTIUDE MEETING BC AT D .AD=X GIVEN
ABD IS A RIGHT ANGLE TRIANGLE WITH ANGLE ADB = 90 ..SO
AB^2=BD^2+AD^2...SINCE THE TRIANGLE IS EQUILATERAL,ALTITUDE IS ALSO THE MEDIAN.HENCE BD=DC=A/2..HENCE
a^2=(a/2)^2+X^2
a^2(1-1/4)=X^2
a^2(3/4)=X^2
a^2=4X^2/3
a=2X/SQRT(3)