Thread: Pythagoras' theorem

A rectangle has a length of 21cm and a diagonal measuring 35cm. Find the area of the envelope.

Can you please also tell me the formula on how to do it please. Thank you

It's the same deal with this question as it was with the other one you posted. We will use Pythagoras' Theorem to find the length of the other side, and then the half-base*height formula for the area of the envelope (which I assume is the "rectangle" mentioned). I hope you realize why we use the two shorter sides to find the area. If not, it's because they are at right angles to each other, so if we places one of the shorter sides on the ground, the other short side would be the vertical height. Anyway, here goes:

Using a^2=b^2+c^2 (Pythagoras' Theorem: a -hypotenuse, b,c-other two sides)
=> a^2-b^2 = c^2
using a=35 cm, b=21 cm, we get
35^2 -21^2 = c^2
784 = c^2
squareroot(784) = c
=> c = 28

For area:
A = 0.5*base*height
= 0.5*21*28
= 294 cm^2

Originally Posted by Jhevon

...For area:
A = 0.5*base*height
= 0.5*21*28
= 294 cm^2

Hello,

I don't want to pick at you but you calculated here by accident the area of a tringle. The area of a rectangle is:

A = length * width

A = 21 * 28 = 588 cm²

EB

You're right! Sorry about that. My bad.

Thanks for looking out EB. You should pick on me for stupid mistakes like that. I almost let chhoeuk turn in bad home work! Sorry chhoeuk.

Originally Posted by Jhevon

Thanks for looking out EB. You should pick on me for stupid mistakes like that. I almost let chhoeuk turn in bad home work! Sorry chhoeuk.

With due respect to incorrect homework, there is no such thing as a "stupid" mistake. Even mistakes can be educational, as I believe this one was.

-Dan

With due respect to incorrect homework, there is no such thing as a "stupid" mistake. Even mistakes can be educational, as I believe this one was.

-Dan ______

In general I would agree with you Dan, but not in this case. Mistakes of this nature shouldn't be made by people doing the math courses I'm doing, especially if they decide to help others. You should be responsible enough to be on your p's and q's when others depend on you. So what was the lesson here? ALWAYS READ THE QUESTION THOROUGHLY BEFORE ATTEMPTING TO ANSWER IT! Did someone benifit from the lesson? I'm sure someone did. But that's a lesson that someone like me should know and follow instinctively, and therefore, at least for me, it was a stupid mistake. But like I said, this is an exception, in general I agree that mistakes can be educational--but that doesn't necessarily mean they're not stupid