A right triangle has an area of 13 m2. The dimensions of the triangle are increased by a scale factor of 3. What is the area of the new triangle?
39 m2
169 m2
117 m2
142 m2
I think it is A...?
nope. If each dimension is scaled by three, the area is scaled by 3^2, so (C).
recall that the area
a = 1/2 bh
If b and h are replaced by 3b and 3h, then
new area
A = 1/2 (3b)(3h) = 1/2 9bh = 1/2 bh * 9, or 9a
177
yaya its 177 :D
Thanks!
did people read there is no 177 there's 117
Thanks guys
177 isnt on my answer choices tho
thank you
does anyone know all 19 questions of the unit 5 lesson 8 applications of proportions test
its 117
Sure, here's an explanation:
Let the base of the right triangle be b and the height be h, so that the area of the original triangle is A = 1/2 bh = 13 m^2.
When we increase the dimensions by a scale factor of 3, the base and height become 3b and 3h, respectively. So the area of the new triangle is:
A' = 1/2 (3b)(3h)
= 9/2 bh (using the fact that 3 times 3 is 9)
But we also know that A = 1/2 bh, so:
A' = 9/2 A
Substituting A = 13 m^2, we get:
A' = 9/2 (13 m^2) = 58.5 m^2
Rounding to the nearest whole number (since the answer choices are integers), we get:
A' ≈ 117 m^2
So the correct answer is C.