What are the length and width of the screen?

Question

The dimensions of a rectangular monitor screen are such that it’s length is 4 inches. More than its width. If the length were doubled and if the width were decreased by 1 inch. The area would be increased by 135 in.². What are the length and width of the screen?

Answer 1

Say w is width

Then l is length

l = w + 4

Area is l w = w (w + 4)

If length is doubled and width decreased by 1, new area is 2l ( w - 1) = (2w + 8) ( w-1).

This must be w (w+4) + 135

(2w+8) ( w-1) = w (w+4) + 135

2w^{2 -}- 2w + 8w - 8 = w² + 4w + 135

w² + 2w - 143 = 0

Solve this for w . (w + 13 ) ( w - 11) = 0 so w= 11, l = 15.

Answer 2

Draw and label a diagram!

(2w + 8)(w - 1) = w(w + 1) + 135

Can you solve for w and answer?

Answer 3

L = w+4

Area = L*w = w(w+4)

doubles the legnth : 2L = 2(w+4)

width decreases by 1 : w-1

then the new area is 2(w+4)(w-1)

Area increases by 135

2(w+4)(w-1) = w(w+4) + 135

2(w^2 + 3w - 4) = w^2 + 4w + 135

2w^2 + 6w - 8 - w^2 - 4w - 135 = 0

w^2 + 2w - 143 = 0

( w + 13 )( w - 11 ) = 0

w+13=0 results in negative measures

w-11 = 0 --> w = 11

original rectangle

length is 15, width is 11 --> area is 165

legth is 30, width is 10, area is 300

which is 135 square units more

length is 15, width is 11 --> area is 165