cxttiemsp021
28.01.2021 •
Mathematics
Help me solve this problem its urgent.....
In the above given figure( attached photo) , M is the point on side QR. Fill in the blanks using symbol =, > or < to complete the statement.
1) PM ____ PQ + QM
2) PM ____ PR + MR
3) PM ____ 1/2 (PQ+PR+QR)
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Ответ:
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 =
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 = and H2 =
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 = = = 1.73 For Triangle 2 lets assign variables C = 3, B = 2 and H2 = = 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
Ответ: