Question

A square and a rectangle have the same area. The length of the rectangle is 8 in. more than a side of the square, and the width of the rectangle is 4 in. less than a side of the square. Find the length of a side of the square.

Answer 1

first of all do you know what is the area of a square?

Answer 2

no

Answer 3

area of a square = side * side

and
area of a rectangle = length * breadth

Answer 4

let the side of the square = a inches

Answer 5

i need to know what the length of the side of the square is.

Answer 6

yes given that:

length is 8 inches more than the side of square = 8+a right?

Answer 7

ya...

Answer 8

also : width of the rectangle is 4 inches less than the side of the square = a-4
right?

Answer 9

I'm really bad at math. i need more help :(

Answer 10

have patience i am helping you ..

Answer 11

ok thank you :D

Answer 12

now we have
length of the rectangle = a+8
and width of the rectangle = a-4

area of the rectangle = length * width = (a+8)(a-4)

but given area of square = area of rectangle
so we have ;:
\[\large{a^2=(a+8)(a-4)}\]

Answer 13

can you tell me what is (a+8)*(a-4)

Answer 14

\[a^{2}+4a-32 ?\]

Answer 15

very good ..
so we have :
\[\large{a^2=a^2+4a-32}\]
\[\large{\textbf{Now dubtract a^2 both sides}}\]

Answer 16

4a-32?

Answer 17

4a-32 = ?

Answer 18

What will be in RHS there...

Answer 19

a-8

Answer 20

no no ..
\[\large{\color{violet}{a^2-a^2=a^2-a^2+4a-32}}\]
\[\large{\color{red}{0=4a-32}}\]

Answer 21

add 32 both sides now

Answer 22

a=8 ?

Answer 23

right

so the side of the square = 8 inches

Answer 24

omg thank you so much C:

Answer 25

best of luck for your journey here in openstudy:
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