Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

If the sum of the legs of a right triangle is 49 inches and the hypotenuse is 41 inches, find the length of the other two sides

Sagot :

naǫ
The length of one leg is x inches.
The sum of the legs is 49 inches, so the length of the other leg is 49-x inches.
The length of the hypotenuse is 41 inches.

Use the Pythagorean theorem:
[tex](\hbox{one leg})^2 + (\hbox{the other leg})^2=(\hbox{hypotenuse})^2 \\ x^2+(49-x)^2=41^2 \\ x^2+2401-98x+x^2=1681 \\ 2x^2-98x+2401=1681 \ \ \ |-1681 \\ 2x^2-98x+720=0 \\ \\ a=2 \\ b=-98 \\ c=720 \\ b^2-4ac=(-98)^2-4 \times 2 \times 720=9604-5760=3844 \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-98) \pm \sqrt{3844}}{2 \times 2}=\frac{98 \pm 62}{4} \\ x=\frac{98-62}{4} \ \lor \ x=\frac{98+62}{4} \\ x=\frac{36}{4} \ \lor \ x=\frac{160}{4} \\ x=9 \ \lor \ x=40[/tex]

[tex] 49-x=49-9 \ \lor \ 49-x=49-40 \\ 49-x=40 \ \lor \ 49-x=9[/tex]

The lengths of the legs are 9 inches and 40 inches.