Acarpet measures 7 ft long and has a diagonal measurment of 8.60 ft . how do i solve to find the width of the carpet?

You can solve this using the Pythagorean theorem.
The Pythagorean therorem states the a^2+b^2(the sides of the triangle adjacent to the right angle) = c^2(the hypotenuse/diagonal)
Now lets plot the information into the Theorem.
7^2+b^2=8.6^2
Solve for b
49+b^2=73.96
b^2=73.96-49
b^2=24.96
b=√(24.96)
b=4.99599839872

The Width would be 4.99599839872 ft.

Hope this helps!