# Math Help - Completing the Square Word Problem

1. ## 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?

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 $(a + b)^2 = a^2 + b^2$. this is wrong!

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

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

3. Forgot about that, thanks for the info.

4. You should learn to type in LaTex. It really makes reading much easier.

\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.

01

5. Dimensions are 18m by 24m.

Only 3 more questions left out of my 122 question project.