Question

a strip of uniform width is to be cut of of both sides and both ends of a sheet of paper that is 7 inches by 10 inches, in order to reduce the size of the paper to an area of 40 square inches find the width of the strip

Answer 1

width = 5 in
length = 8 in
both sides cut 2 in

Answer 2

Can you explain to me how you got this?

Answer 3

width of the strip is one inch
two cuts along 10 inch length eqals 20 sq ing
then two cuts along width eqials 10 - reduced by 30 to give 5*8 = 40 sq ins

one inch strip

Answer 4

let us assume we cut x in
therefore the width is 7- x
and length is 10-x
hence area (7-x)(10-x) = 40
on solving for x
x^2 -17x + 30 = 0
solve for x = 2 or -15 ( but x cannot be negative)
so x = 2 in
width = 7- 2 = 5 in
lenght = 10- 2 = 8 in

Answer 5

thanks sheg you are awesome!

Answer 6

sorry one mistake x = 15 or 2
but lenght is equal to 10 inches and width = 7 inches
hence x = 15 rejected

Answer 7

the question said that the strips were to come from both sides and both ends of the paper thats why i said 1 inch.
If strip is only taken from one end and one side then the answer is 2 ins.

Answer 8

Let the uniform width of the strip to be cut = x inch
since it is to be cut from both sides and both ends, hence

new length becomes = 10 - x - x = 10 - 2x
and new width becomes = 7 - x - x = 7 - 2x

ATQ (10-2x)(7-2x) = 40
70 - 14x - 20x + 4x^2 = 40
4x^2 - 34x + 30 = 0 dividing throughout by 2
2x^2 - 17x + 15 = 0
2x^2 - 2x - 15x + 15 = 0
2x(x - 1) -15(x - 1) = 0
(x - 1)(2x - 15) = 0
if x -1 = 0, then x = 1
if 2x - 15 = 0, then x = 15/2 => x = 7.5

Now you cannot cut strips of 7.5 in from both ends of a paper only 7 inch wide, hence this value of x is not workable.

Hence x = 1 is the right value

So the uniform width of the strip which cabe cut from both ends and bot sides is 1in.

Answer 9

*So the uniform width of the strip which can be cut from both ends and bot sides is 1in.

You can check that this is the right answer.....

Answer 10

u ppl are talikng over this thing tell me one thing if i will cut 2 inches from all the sides what will happen width will get reduced to 3 in and length to 6 inches
so its obvious that we will cut in total 2 inches from both sides i.e. 1 inch from one side and 1 inch from the other and like wise