QR question

[Lonely Sol]

I remembered how to do this a while back, but just cant figure it. Any help would be greatly appreciated, thanks:

A Triangle ABC is similar to Triangle DEF; AB is 4 units long and DE is 8 units long. If Triangle ABC has area of 10 square units, what is the area of Triangle DEF in square units?

a. 3.2
b. sqrt(80)
c. sqrt(200)
d. 20
e. 40

The answer is e.

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[Nasem]

(4/8) = (10/x)

OR

(8/4) = (x/10)

and solve for x

 

[Streetwolf]

Each dimension is multiplied by a factor of 2, so the area is multiplied by a factor of 4.

Answer is 10 x 4 = 40 (e)

Edit: Nasem beat me with posting but that's not how you do it.

 

[zreyes86]

Draw the two triangles and make AB=4 the base of triangle ABC and DE=8 the base of triangle DEF. Start with triangle ABC, since you know the base and the total area (10) you can solve for height using A=(bh)/2. The height of triangle ABC is 5. Once you know the height you can use this information for triangle DEF. Since AB is twice DE, the height of triangle DEF must also be twice that of triangle ABC. Therefore, the height of triangle DEF is 10. If you plug the base (8) and the height (10) into the A=(bh)/2 formula, you get A=40 for triangle DEF.

 

[Lonely Sol]

Thanks for the reply, really appreciate it! One question, how do you know that area is the factor of four, i mean is there any equation that make sense or anything!

 

[gigit]

Thanks for the reply, really appreciate it! One question, how do you know that area is the factor of four, i mean is there any equation that make sense or anything!

Geometry basically deals with three fundamental dimensions, which are 1D (linear), 2D (area), and 3D (volume).

Examples:

1D : length (l)

2D : area like l x w for a rectangle, s x s for square, 1/2 x h x b for a triangle

3D : volume like 4/3 pi x r^3 for a sphere, s x s x s for a cuboid

Ignoring all constant and coefficient that may come along with the formula, you'll notice that 1D deals with 1st degree of measurement, whereas 2D and 3D are related to 2nd and 3rd degree respectively.

In the question you posted here, doubling one side of the smaller triangle will double rest of other parts to make the bigger triangle similar or congruent.

Hence, your h1 = 2h, and b1 = 2b

This makes the ratio of the area:

1/2 x 2h x 2b : 1/2 h x b ---> 4 : 1

To test yourself whether you've understood what I explained here. Tell me what factor of increase in area if AB is 4 units long and DE is 6 units long this time round?

 

[CyborgNinjaX]

I skimmed over the other replies but here is what I did:

Triangle #1: one side is 4 units, area is 10 units
Triangle #2: one side is 8 units, area is unknown

Area = .5bh
10 = .5(4)h
h = 5

8/4 = 2 (triangle #2 has a ratio of 2:1 to triangle #1, meaning the sides are 8 units and 10 units respectively)

Area = .5(10)8
Area = 40 units