A rectangular phone is 3 cm longer than it is wide. The photo is surrounded with a wooden frame that is 2cm wide on all sides. The area of the frame is 52 square centimeters. Find the dimensions of the photo.

the width is 3.9

the length is 3+w= 3+3.9 =6.9

Step-by-step 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

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,