Question

The height of triangle A is 50% of the width of rectangle B. If the area of triangle A is 4, what is the area of rectangle B

Answer 1

not enough information. There's no relationship between the length of the rectangle and the base of the triangle.

Answer 2

area of the rectangle will be 16

Do u want the working??

Answer 3

Area of the rectangle can't be found since no length of the rectangle is mentioned.

Answer 4

We could look at it like in the pic.

Each triangle within the rectangle has height 50% of the width of the rectangle and area 4 for a total of 16.

How about that?

Answer 5

So what do we think?

Answer 6

But it says that the height of the triangle is half the width......

I solved it as follows:

Answer 7

Yes, I just turned the triangles around.

Answer 8

I'm not sure if the tack u r taking is correct....

I solved it as follows:

Answer 9

It satisfies all the conditions....

Answer 10

In my attached figure the height XY of the triangle is half of the width AD

Now through the point X draw EF parallel to AB.

so now rectangle ABCD is divide into two rectangles AEFB and EDCF of equal area wich is half that of original rectangle ABCD

Now rectangle EDCF is also a parallelogram.

Here we apply the theorem that "If a triangle and a ||gm are on the same base and between the same parallels, then the area of the triangle is half that of the ||gm."

Since triangleXDC and ||gm share the same base DC and lie between the same parallels DC and EF, so area of triangle XDC is half the area of rectangle EDCF.
=> area of EDCF = 2 * Area of triangleXDC = 2*4 = 8

so area of rectangle ABCD = 2*area of rectangle EDCF = 2*8 = 16

Answer 11

Yes, but you are assuming that the triangle and the //gram are on the same base and between the same //'s which is not a given in the question.

Answer 12

The parallel line we get due to construction as I explained above....
Since X is at a height half the width a line through it drawn parallel to one of the sides of the rectangle will result in a parallelogram

In your solution too, you have made an assumption about the length of the triangle becoz nothing is said about the length. i am sure the question was accompanied by a figure which the asker did not send....

Answer 13

I haven't made an assumption like that, if

4 = 1/2 * base * height, then h = 8/base and within the confines of the question I can choose freely which is base and which is height.

Answer 14

Think you're right about the diagram, though,,,,:-)

I just though it was interesting to consider it without.

Answer 15

well by that argument...
4 = 1/2 * b *h means base of my rectangle is 8/h where h is the height of the triangle
also the width of the rectangle is twice the height of triangle means that width of rectangle is 2h
area of rectangle = 2h * 8/h = 16

Answer 16

Agreed.

Answer 17

Well at least we agree that the answer is 16 ☺☻

I guess the people who ask questions shud put the full question along with given diagram so that we know what approach to take....