Answer:
the width is 3.9
the length is 3+w= 3+3.9 =6.9
Explanation:
A photo is rectangular with 3cm longer than its width
meaning length is 3+w(3 plus the dimension of the width)
area = length x breadth = (3+w)w=3w+w²=w²+3w
A frame housing the photo is 2cm wide on all sides
meaning the length is 3+w+2
the width is w+2
area of the frame is 52cm²
area of frame = length x breadth
area of frame= (3+w+2) * (w+2)
area of frame = (5+w)x(w+2) =w(5+w)+2(5+w)= 5w+w²+10+2w
area of frame= 5w+2w+w²+10= 7w +w²+10=w²+7w+10
area of frame= w²+7w+10
52 = w²+7w+10
w²+7w+10-52=0
w²+7w-42=0
using quadratic formula
x=-b±√b2-4ac/2a
b= 7
c=-42
a=1
x= -7±√7²-4(1)(-42)/2(1) = -7±√49+168/2
x=-7±√217/2= -7±14.7309198627/2
x= -7+14.73/2 x= -7-14.73/2
x=7.73/2 -21.73/2
x= 3.865, -10.865
since a dimension can not be negative e neglect the negative sign
x=3.9
the width is 3.9
the length is 3+w= 3+3.9 =6.9