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The shortest distance between planet Q and planet R is [tex]1.64 \times 10^7\ km[/tex]
The distance between points is the number of units between them
The distances between some planets are given as:
[tex]QP = 3.6 \times 10^6[/tex]
[tex]RP = 1.6 \times 10^7[/tex]
The shortest distance (x) is then calculated using the following Pythagoras theorem
[tex]x^2 = RP^2 + QP^2[/tex]
This gives
[tex]x^2 = (3.6 \times 10^6)^2 + (1.6 \times 10^7)^2[/tex]
Evaluate the squares
[tex]x^2 = 12.96 \times 10^{12} + 2.56 \times 10^{14}[/tex]
Rewrite as:
[tex]x^2 = 12.96 \times 10^{12} + 256 \times 10^{12}[/tex]
Evaluate the sums
[tex]x^2 = 268.96\times 10^{12}[/tex]
Take square roots of both sides
[tex]x = 16.4\times 10^{6}[/tex]
Rewrite as:
[tex]x = 1.64\times 10^{7}[/tex]
Hence, the shortest distance between planet Q and planet R is [tex]1.64 \times 10^7\ km[/tex]
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