The side lengths of the given right triangle are 6m and 8m respectively.
What is a right triangle?
A right triangle is a triangle that has an interior angle of right angle.
Given, the hypotenuse of a right triangle is 10 m.
Let, the shorter leg is x m.
Therefore, the other leg is (x + 2) m.
Now for the given right triangle, [tex]x^{2} + (x+2)^{2} = 10^{2}[/tex]
⇒ [tex]x^{2} + x^{2} +4x + 4= 100[/tex]
⇒ [tex]2x^{2} +4x + 4 - 100 = 0[/tex]
⇒ [tex]2x^{2} +4x - 96 = 0[/tex]
⇒ [tex]x^{2} + 2x - 48 = 0[/tex]
⇒ [tex](x+8)(x-6) = 0[/tex]
⇒ [tex]x = 6[/tex] (ignoring the negative value)
Therefore, the shorter leg is 6 m.
Now, the other leg is
[tex](6+2)m\\= 8 m[/tex]
Learn more about a right triangle here: https://brainly.com/question/6846590
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