# Completing the Square Word Problem

• Jun 14th 2009, 01:00 PM
Completing the Square Word Problem
Alright I'm not exactly sure what category this question falls under, but it was a question part of a "completing the square" unit.

A rectangle is 6m longer than wide. The diagonal is 30m. Find the dimensions of the rectangle.

I drew a diagram, L representing Length and W representing Width.

(w)^2+(w+6)^2=(30)^2
w^2+w^2+36=900
w^2+w^2=900-36
2w^2=864
w^2=432
w=sqrt 432
w=20.8m

Then I subbed w=20.8m into L = W +6 to find L.

L = 26.8M

So the dimensions were 20.8m and 26.8m. For some reason this doesn't look right. No completing the square was involved in this question. Is my answer correct?
• Jun 14th 2009, 01:03 PM
Jhevon
Quote:

Alright I'm not exactly sure what category this question falls under, but it was a question part of a "completing the square" unit.

A rectangle is 6m longer than wide. The diagonal is 30m. Find the dimensions of the rectangle.

I drew a diagram, L representing Length and W representing Width.

(w)^2+(w+6)^2=(30)^2
w^2+w^2+36=900
w^2+w^2=900-36
2w^2=864
w^2=432
w=sqrt 432
w=20.8m

Then I subbed w=20.8m into L = W +6 to find L.

L = 26.8M

So the dimensions were 20.8m and 26.8m. For some reason this doesn't look right. No completing the square was involved in this question. Is my answer correct?

common mistake: thinking that $\displaystyle (a + b)^2 = a^2 + b^2$. this is wrong!

rather, $\displaystyle (a + b)^2 = a^2 + 2ab + b^2$

hence $\displaystyle (w + 6)^2 = w^2 + 12w + 36$

• Jun 14th 2009, 01:16 PM
Forgot about that, thanks for the info. :)
• Jun 14th 2009, 02:24 PM
yeongil
You should learn to type in LaTex. It really makes reading much easier. (Wink)

\displaystyle \begin{aligned} w^2 + (w + 6)^2 &= 30^2 \\ w^2 + w^2 + 12w + 36 &= 900 \\ 2w^2 + 12w + 36 &= 900 \\ 2w^2 + 12w &= 864 \\ w^2 + 6w &= 432 \\ \end{aligned}
^ Here is where you should complete the square. I'll leave the rest up to you.

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• Jun 14th 2009, 02:37 PM