Question

The length of a rectangular painting is 3 inches longer than its width. If the diagonal is 15 inches long, what is the length of the painting

Answer 1

a^2+b^2= 15^2

b=a-3

Use substitution
a^2+(a-3)^2= 225
a^2+a^2-6a+9=225
2a^2-6a=-216
2a^2-6a+216=0

2(a^2-3a+108)
2(a-12)(a+9)

(a-12)=0
a=12
(a+9)=0
a=-9
A is -9 or 12, but since an object can't have a negative length or width, a must be 12.

Plug this value of a in.
b=(12)-3
b=9

Final answer: Length=9, width=12

Answer 2

the previous answer is wrong, the length of the painting is 12 inches.