[SPLIT] If the length of one side of a square is increased by 6cm and...

[Mz513]

If the length of one side of a square is increased by 6cm and the length of the adjacent side of the square is doubled, a rectangle is formed having an area that is 13cm ² greater than the area of the original square. Determine the length of one side of the square......

I don't know where to start somebody help!!!

 

[Romsek]

If the length of one side of a square is increased by 6cm and the length of the adjacent side of the square is doubled, a rectangle is formed having an area that is 13cm ² greater than the area of the original square. Determine the length of one side of the square......

I don't know where to start somebody help!!!

let a side of your original square have length s. The original area is then A = s².

then (s + 6)(2s) = A + 13 = s² + 13

so (s + 6)(2s) = s² + 13

solve that for s

 

[Mz513]

let a side of your original square have length s. The original area is then A = s².

then (s + 6)(2s) = A + 13 = s² + 13

so (s + 6)(2s) = s² + 13

solve that for s

Thank you you in new didn't know where to post here!!

 

[Mz513]

Still confused

let a side of your original square have length s. The original area is then A = s².

then (s + 6)(2s) = A + 13 = s² + 13

so (s + 6)(2s) = s² + 13

solve that for s

I still ill feel like I don't understand I need more help please!!

 

[Mz513]

So is the side squared
12²

 

[Romsek]

I still ill feel like I don't understand I need more help please!!

You have an original square that has sides length s cm. This square has area A1 = s * s = s² (cm)²

Ok?

Your problem says you take one side and make it longer by 6cm. That becomes (s + 6) cm

It also says take an adjacent side and double it's length. That becomes 2s cm

This is now a rectangle that has area A2 = (2s) * (s+6) = 2s² + 12s

This new area A2 is 13cm² larger than the original area A1.

so A2 = A1 + 13

substituting for A2 and A1

2s² + 12s = s² + 13

doing a bit of algebra we get

s² + 12s - 13 = 0

a clever eye sees this can be written as (s + 13)(s - 1) = 0, which is solved by s = -13cm, or s = 1 cm
you could also use the quadratic formula to solve this.

You can't have the side of a square equal to -13 cm, so it must be that s = 1 cm

Checking we find A1 = 1, A2 = 7*2 = 14 = 1 + 13 = A1 + 13

and we see that the correct answer is indeed s = 1 cm

I really can't make it any clearer than this.