Multiple choice geometry question

Two similar triangles have a ratio of similitude (scale factor) of 3:5. What is the ratio of their areas?

A. 3:5
B. 2:3
C. 9:25
D. None of the above

area is ratio squared.

it would be 3:5squared, so...
C. 9:25.(:

The answer is C. 9:25
To find this, draw 2 right triangles.
One has side lengths 3 and 6, and the other has side lengths 5 and 10 (because of the 3:5 scale factor).
Use A=½bh to find that the first triangle has an area of ½(6)(3)=3*3=9 and the second triangle has an area of ½(10)(5)=5(5)=25.
Therefore the ratio of their areas is 9:25.

The formula for the area of a triangle is 1/2bh
The first triangle has a base of 3b and height of 3h
The second triangle would have a base of 5b and a height of 5h

The first triangle's area is 1/2(3b x 3h)
1/2 (9bh)
The second has 1/2(5b x 5h)
1/2 (25bh)

Therefore, the ratio is C. 9:25

area = 1/2 * base * altitude.

so,

if similitude ratio is 3: 5, then

their area = 1/2*b*a

suppose triangle 1 , a=3 b= 3 & in triangle 2, b=5 & a= 5 [3:5 ratio / scale factor}

area of triangle 1 = 1/2 *3*3 = 9/2 sq unit

area of triangle 2 = 1/2 * 5*5 = 25/2

so,

ratio of area

A1: A2 = 9/2 by 25/2

= (9*2) / (25*2)

= 9 /25 = 9:25

ans C

Take 2 right-triangles.

Triangle 1) 3,4,5 meets pythagorean theorem. So lets say it's height 3 and base 4, hypotenus 5

Lets say the first one has sides 3, 4, 5. Area would be 1/2 base * Height

so 1/2 (4) * 3 That's area of 6


Triangle 2 would be 3*(5/3) ,4*(5/3), 5*(5/3) = Height 5, Base 20/3, hypotenus 25/3

so we need 1/2 (20/3) * 5 = 10/3 * 5 = 50/3

so we have 6/ 50/3 which is 18/50 = 9/25

9:25 C

If two similar triangles have a scale factor of a : b,
then the ratio of their areas is a^2 : b^2.

scale factor = 3:5
ratio of their areas = 3^2 : 5^2 = 9:25 (C)

the scale factor is a measure of the linear dimensions...area is a squared measure...

the ratio of the areas is: 9 : 25

@Σ

C

D none above