Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Calculate the value of x

A wedge of cheese is in the shape if a prism.
It is cut into two equal volumes by a single cut, parallel to one face.
The base of the larger triangular face is 24cm.
Tha base of the smaller triangular face (i.e. after being cut) is x cm
The width of the wedge is 10cm.
Calculate the value of x.

Can anyone help me with this? im in the middle of my gcses.. and its from a gcse textbook and its really bugging me! Im sure there is a simple way of doing it, but the fact that it doesn't give you the height confuses me a little - I've tried using algebraic terms for the heights of both triangles, but it doesn't get me anywhere.

Thanks.

Last edited by Daniel123 (2007-05-23 20:26:51)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Calculate the value of x

Well, we can ignore the third dimension for a start. It's a prism, so if the answer is right for its cross-sectional area then the answer will be right for it as well. But it sounds like you might have been doing that anyway.

I suspect that the answer will always be the same, no matter what the height is. So if we just say that the height is an arbitrary amount h, then hopefully it will cancel out at some point.

A triangle with length 24 and height h will have an area of 1/2*24*h = 12h.
We want to find the value of x such that the smaller triangle will have area 6h.

By similar triangles, a triangle with length x will have a height of hx/24.
Therefore, its area will be hx²/48.

hx²/48 = 6h
x² = 288
x = √288 = 12√2

---

Why did the vector cross the road?
It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Calculate the value of x

Thanks mathsyperson!

I totally understand it now!

I didn't think to use similar triangles!

thankssss