Problema Solution
A rectangular picture is 4 cm longer than it is wide. It is surrounded by a mat that is 2 cm wide. The combined area of the mat is 140 cm(squared). Find the dimensions of the picture.
Answer provided by our tutors
area = length * width
for the picture, l = w + 4
the mat extends 2 cm beyond the picture, therefore the combined area is given by this equation:
(w+6)(w+2)=140
simplying gives:
w^2 + 8w -128 = 0
solving for 'w' gives w=8 as the positive answer
so the picture is 8 cm wide and (8+4)=12 cm in length