QUESTION 1
Let the third side of the right angle triangle with sides be
.
Then, from the Pythagoras Theorem;
Let the hypotenuse of the right angle triangle with sides 2,6 be .
Then;
Using the bigger right angle triangle,
Group similar terms;
QUESTION 2
Let the hypotenuse of the triangle with sides (x+2),4 be .
Then,
Let the hypotenuse of the right triangle with sides 2,4 be .
Then; we have
We apply the Pythagoras Theorem to the bigger right angle triangle to obtain;
QUESTION 3
Let the hypotenuse of the triangle with sides (x+8),10 be .
Then,
Let the hypotenuse of the right triangle with sides 5,10 be .
Then; we have
We apply the Pythagoras Theorem to the bigger right angle triangle to obtain;
QUESTION 4
Let the height of the triangle be H;
Then
Let the hypotenuse of the triangle with sides H,x be r.
Then;
This implies that;
We apply Pythagoras Theorem to the bigger triangle to get;
This implies that;
QUESTION 5
Let the height of this triangle be c.
Then;
Let the hypotenuse of the right triangle with sides x,c be j.
Then;
We apply Pythagoras Theorem to the bigger right triangle to obtain;
QUESTION 6
Let the height be g.
Then;
Let the hypotenuse of the triangle with sides g,24, be b.
Then
We apply Pythagaoras Theorem to the bigger right triangle to get;
This implies that;
Take the positive square root of both sides.
QUESTION 7
Let the hypotenuse of the smaller right triangle be; n.
Then;
Let f be the hypotenuse of the right triangle with sides 2,(x+3), be f.
Then;
We apply Pythagoras Theorem to the bigger right triangle to get;
We are dealing with length.
QUESTION 8.
We apply the leg theorem to obtain;
We discard the negative value;
QUESTION 9;
We apply the leg theorem again;
Factor;
Discard the negative value;
QUESTION 10
According to the leg theorem;
The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the portion of the hypotenuse adjacent to that leg.
We apply the leg theorem to get;
units.
QUESTION 11
See attachment
Question 12
See attachment
