A right triangle is shown below.
a=6
b=8
c=?
The triangle is dilated by a scale factor of 2.5 to create a new triangle. What is the perimeter of the new triangle?
answs; 120,24,60 and 150
i keep getting different answers can someone help?
I assume that c is the hypotenuse.
c^2 = a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100
so
c = 10
(note, this is a 3,4,5 triangle scaled up by 2 so the answer was known before we started)
Now linera dimensions like perimeter scale with the scale ratio
original perimeter = 6 + 8 + 10 = 24
new perimeter = 2.5 * 24 = 48+12 = 60
To find the perimeter of the new triangle, we first need to calculate the lengths of the sides of the new triangle after it has been dilated by a scale factor of 2.5.
The original right triangle has side lengths a = 6 and b = 8. The length of the hypotenuse, c, can be calculated using the Pythagorean theorem: c = √(a² + b²).
c = √(6² + 8²)
c = √(36 + 64)
c = √100
c = 10
So, the original triangle has side lengths a = 6, b = 8, and c = 10.
To dilate the triangle by a scale factor of 2.5, we need to multiply each side length by 2.5:
New side length a' = 6 * 2.5 = 15
New side length b' = 8 * 2.5 = 20
New side length c' = 10 * 2.5 = 25
Now that we have the side lengths of the new triangle, we can find its perimeter by adding all three sides together:
Perimeter of the new triangle = a' + b' + c'
Perimeter = 15 + 20 + 25
Perimeter = 60
Therefore, the perimeter of the new triangle after being dilated by a scale factor of 2.5 is 60.