Answer:
[tex]x^2 = 15^2 - 9^2[/tex]
Step-by-step explanation:
So we are given a rectangle whose width is 9 units, length is x units, and diagonal is 15 units.
Let us draw a diagram based on the above information.
Refer to the attached diagram, as you can notice there is a right angled triangle which means we can apply Pythagorean theorem to find out the value of unknown side x.
Recall that Pythagorean theorem is given by
[tex]$c^2 = a^2 + b^2$[/tex]
From the diagram, we have
c = 15
a = 9
b = x
So the equation becomes,
[tex]$15^2 = 9^2 + x^2$[/tex]
[tex]x^2 = 15^2 - 9^2[/tex]
So this the correct equation!
Bonus:
The value of length x is
[tex]x^2 = 15^2 - 9^2 \\\\x^2 = 225 - 81 \\\\x^2 = 144\\\\x = \sqrt{144}\\\\x = 12 \: units[/tex]
