Create a right isosceles triangle, where the two side lengths are 12cm. What is the length of the third side of the triangle?
Answers
Answer:
improper question plz chk?
may be your question is
Create a right isosceles triangle, where the two side lengths are 12cm and 5cm. What is the length of the third side of the triangle?
There are actually two solutions to this problem!
We know that A=12bh=12 , and that a vertical line from the apex of the triangle to the base will divide it into two congruent right triangles, each with base 12b , height h , and hypotenuse 5.
However, to make the math a little simpler, I’m going to define a new variable, c=12b , so A=ch=12 , and each right triangle has a height of c .
From there, the Pythagorean theorem tells us:
c2+h2=52
By this point, you might have already figured out what two numbers multiply to make 12, and make a Pythagorean triple with 5, but let’s continue!
Solving the area equation for h , we get h =12c . Substituting that expression into the Pythagorean equation, we get:
c2+(12c)2=25
Multiplying through by c2 , we get:
c4+144=25c2⟹c4−25c2+144=0
We can factor that into (c2−9)(c2−16)=0 , and solve those two expressions to get:
c={±3,±4}
The negative values have no meaning in the context of triangle dimensions, so c={3,4) .
Returning to c=12b , b=2c={6,8} . That is, the possible solutions are:
Base of 6 cm, height of 4cm
Base of 8 cm, height of 3 cm
Answer:
12√2
Step-by-step explanation:
according to PYTHAGORAS THEOREM ,
(perpendicular )² + ( base )² = ( hypotenuse )²
( 12 )² + ( 12 )² = ( hypotenuse )²
hypotenuse = 12√2