# Thread: Rectangle is Inscribed (Did I do it right?)

1. ## Rectangle is Inscribed (Did I do it right?)

Hi I am working on this Optimization Question but like usual, I am never sure if I am doing it right.

The question is:
A rectangle is inscribed in a semi circle of radius 25cm. Find the largest area of such a rectangle.

Here is what i have done so far:

Can someone tell me what steps I have done wrong? And what should I do next?

Thanks

2. Originally Posted by asemh
Hi I am working on this Optimization Question but like usual, I am never sure if I am doing it right.

The question is:
A rectangle is inscribed in a semi circle of radius 25cm. Find the largest area of such a rectangle.

Here is what i have done so far:

Can someone tell me what steps I have done wrong? And what should I do next?

Thanks
1. The labeling in the drawing should have 2x as length of the rectangle. The 2nd line should read: $x^2+y^2=25^2$

2. All calculations are OK. Calculate now y and A.

3. To find y,

I plugged my x into y = sqrt(625 - x^2) and got 17.68
when i plugged it into my area formula i got 625

Would that be the correct answer?

4. Originally Posted by asemh
To find y,

I plugged my x into y = sqrt(625 - x^2) and got 17.68
when i plugged it into my area formula i got 625

Would that be the correct answer?
Yes