Thread: Algebra

1) The two sides of the right angle have lengths x and y. Represent the change in the triangle's area if the length of one side is doubled and the length of the other side is halved.

2) The two equal sides of an isosceles triangle each have a length of 2x+3y-1. The perimeter of the triangle is 7x+9y. Determine the length of the third side.

Originally Posted by darkangel06

1) The two sides of the right angle have lengths x and y. Represent the change in the triangle's area if the length of one side is doubled and the length of the other side is halved.

2) The two equal sides of an isosceles triangle each have a length of 2x+3y-1. The perimeter of the triangle is 7x+9y. Determine the length of the third side.

Hi darkangel06!

A rectangular triangle with sides x and y has an area of (1/2)xy.
If I double x and half y, I get a rectangular triangle with sides (2x) and (1/2)y.
Can you tell what the area is of that second triangle?

for the second one they did not mention the area of the triangle

Originally Posted by darkangel06

for the second one they did not mention the area of the triangle

No, I didn't get to the second one yet.
I decided to start with just the first one hoping for some feedback from you.

Oh! For the first one the area is just 0

Originally Posted by darkangel06

Oh! For the first one the area is just 0

How did you get an area of 0?
A triangle will always have an area that is greater than 0...

Well, that's what the answer is in the textbook and that's what i'm tryin to figure out :/

Originally Posted by darkangel06

Well, that's what the answer is in the textbook and that's what i'm tryin to figure out :/

Ah! The change in area is 0 according to the answer in your textbook.
But then you didn't answer my question yet: if I have a rectangular triangle with sides (2x) and (1/2)y, what is its area?

there is no area mentioned in the question !!!

Originally Posted by darkangel06

1) The two sides of the right angle have lengths x and y. Represent the change in the triangle's area if the length of one side is doubled and the length of the other side is halved.

Originally Posted by darkangel06

there is no area mentioned in the question !!!

Yes there is! See bolding.

I know. But the area is actually zero. That's what we have to find out. How is it zero.

Originally Posted by darkangel06

I know. But the area is actually zero. That's what we have to find out. How is it zero.

Well, that was my point.
The area is not zero.
A triangle never has a zero area.
In particular, the area of a rectangular triangle is .

What do you get if you replace by and by ?

It is a right angle not a rectangular triangle.

Originally Posted by darkangel06

It is a right angle not a rectangular triangle.

I guess I should have called it a right triangle.
Sorry, I'm not natively Canadian.
I meant a triangle like the one in my avatar.

Oh wait!
I meant I'm not natively Kuwaitian.
(I had just looked up Brampton - first hit was Canada.)