Question

The distances between some planets are given below.


Planet Q is 3.6 x 10 to the power of 6 km from planet P.

Planet R is 1.6 x 10 to the power of 7 km from planet P.


Work out the shortest distance between

planet Q and planet R.

Give your answer in standard form.

Answer 1

The shortest distance between  planet Q and planet R is $1.64 \times 10^7\ km$

Distance

The distance between points is the number of units between them

The distances between some planets are given as:

$QP = 3.6 \times 10^6$

$RP = 1.6 \times 10^7$

Shortest distance

The shortest distance (x) is then calculated using the following Pythagoras theorem

$x^2 = RP^2 + QP^2$

This gives

$x^2 = (3.6 \times 10^6)^2 + (1.6 \times 10^7)^2$

Evaluate the squares

$x^2 = 12.96 \times 10^{12} + 2.56 \times 10^{14}$

Rewrite as:

$x^2 = 12.96 \times 10^{12} + 256 \times 10^{12}$

Evaluate the sums

$x^2 = 268.96\times 10^{12}$

Take square roots of both sides

$x = 16.4\times 10^{6}$

Rewrite as:

$x = 1.64\times 10^{7}$

Hence, the shortest distance between  planet Q and planet R is $1.64 \times 10^7\ km$

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