Question

the length of a rectangle is 10 more than the side

of a square, and the width if the rectangle is 10

less than the side of the square. If the area of

the square is 125, what is the area of the

rectangle?

Answer 1

and the width of the rectangle is 10 less than the side of the square.

Answer 2

what is the formula for the area of a square?

Answer 3

s squared

Answer 4

I think that one side would be the square root of 125

Answer 5

the square roots of 125 squared is 125

Answer 6

very good, although you must say what s means,. s, in this case, means the side of a square..

Answer 7

yes

Answer 8

right, very good. That means the side of the square is the square root of 125.

Answer 9

so the length of the rectangle should be the square root of 125 plus 10

Answer 10

yup, and what about the width?

Answer 11

that equals 21.18033989

Answer 12

the width

Answer 13

1.180339887?

Answer 14

no no. you dont need to know the value 21.18033989, because I know some magic is going to happen.

Answer 15

I got 25.74

Answer 16

Okay. You are correct, but I know of a better way to solve this problem. Are you with me?

Answer 17

So I would round it to 25

Answer 18

sure

Answer 19

\[length = \sqrt{125} + 10\]

Answer 20

yep

Answer 21

\[width = \sqrt{125} -10\]

Answer 22

yep

Answer 23

area of a rectangle is length times width. so,\[area = (\sqrt{125}+10) \times (\sqrt{125}-10)\]

Answer 24

125-100?

Answer 25

now, there is a little formula which says \[(a+b) \times (a-b) = a ^{2} - b ^{2}\]

Answer 26

excellent. You are right. see how didnt need to use a calculator?

Answer 27

the different of two squares?

Answer 28

yep

Answer 29

Cool