Answer:
[tex]\boxed {\tt b=24 \ centimeters}[/tex]
Step-by-step explanation:
This is a right triangle, so we can use Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
a and b are the legs, while c is the hypotenuse.
One leg is 10 centimeters. The hypotenuse is 26 centimeters. Therefore,
[tex]a= 10 \ cm \\c= 26 \ cm[/tex]
[tex](10 \ cm )^2+b^2=(26 \ cm)^2[/tex]
Solve the exponents.
- (10 cm)²= 10 cm * 10 cm= 100 cm²
[tex]100 \ cm^2+b^2=(26 \ cm)^2[/tex]
- (26 cm)²= 26 cm * 26 cm= 676 cm²
[tex]100 \ cm^2+b^2=676 \ cm^2[/tex]
Subtract 100 from both sides of the equation.
[tex]100 \ cm^2- 100 \ cm^2+b^2=676 \ cm^2- 100 \ cm^2[/tex]
[tex]b^2=676 \ cm^2 - 100 \ cm^2[/tex]
[tex]b^2= 576 \ cm^2[/tex]
Take the square root of both sides of the equation.
[tex]\sqrt{b^2} =\sqrt{576 \ cm^2}[/tex]
[tex]b=\sqrt{576 \ cm^2}[/tex]
[tex]b= 24 \ cm[/tex]
The other leg of the triangle is equal to 24 centimeters.
