Question

Help me solve this problem its urgent.....

Answer 1

Answer:

1) PM < PQ + QM

2) PM < PR + MR

3) PM < 1/2 (PQ + PR + QR)

Step-by-step explanation:

This problem is based on the Pythagorean Theorum Equation

which states that a right triangle with sides a, b and hypotenuse can be written mathematically as hypotenuse = $\sqrt{a^2 + b^2}$

We can rewrite each line segment of the diagram into variables to simplify this problem and use the Pythagorean equation:

Line PQ = Hypotenuse 1, Line PR = Hypotenuse 2, Line PM = Side B, Line QM = Side A, Line MR = Side C

With all the line segments simplified into variables you can separate the diagram into 2 seperate triangles. Triangle 1 has H1, A, B and Triangle 2 has H2, C, B

Using the Pythagorean equation for both triangles you get:

H1 = $\sqrt{a^2 + b^2}$   and H2 = $\sqrt {c^2 + b^2}$  

Now you can assign random values for each variable and compare the problem statements.

For Triangle 1 lets assign variables A = 1, B = 2, and H1 = $\sqrt{1^2 + 2^2}$ = $\sqrt{3}$ = 1.73  For Triangle 2 lets assign variables C = 3, B = 2 and H2 = $\sqrt {3^2 + 2^2} = \sqrt {13}$ = 3.6  

For the final step you can directly compare the statements and see which symbol is correct.

1) B ____ H1 + A is equivalent to  2  ____ (1.73 + 1),  which is turns out to be  2 < 2.73   The answer is  <

2) B ____ H2 + C is equivalent to 2 ____ (3.6 + 3), which turns out to be

2 < 6.6    The answer is < again

3) B ____ 1/2 (H1 + H2 + (A+C)  is equivalent to  2 _____ [1/2] (1.73 + 3.6 + 1 + 3), which turns out to be  2 < 4.67     The answer is <  again