Question

a rectangle has a diagonal that measures 10 centimeters and a length that is 2 centimeters longer than the width. What is the width of the rectangle in centimeters?

Answer 1

6

Answer 2

you could use Pythagorean theorem

Answer 3

\[\sqrt{x^2+y^2}=10\]
\[x=y+2\]
\[2y^2+4y+4=100\]
\[y^2+2y-48=0\]

Answer 4

\[10^2-(2+w)^2=w^2\]
\[100-(4+4w+w^2)=w^2\]
\[100-4-4w-w^2=w^2\]
\[2w^2+4w-96=0\]
\[w^2+2w-48=0\]
\[(w+8)(w-6)\]
\[w=-8, w=6\]
Reject -8 as it is negative and you cannot have a negative length.