A right triangle has an area of 13 m^2. The dimensions of the triangle are increased by a scale factor of 3. What is the area of the new triangle?
A. 39 m^2
B. 169 m^2
C. 117 m^2***
D. 142 m^2
Am I right?
Thank you Again
zat ees courrect.
To find the area of the new triangle after the dimensions are increased by a scale factor of 3, you need to square the scale factor and then multiply it by the original area of the triangle.
The scale factor of 3 means that each side of the triangle is multiplied by 3. Since the area of a right triangle is given by the formula (base * height) / 2, the new area can be calculated as follows:
New Area = (original base * scale factor) * (original height * scale factor) / 2
Simplifying this equation, we have:
New Area = (3 * original base) * (3 * original height) / 2
Now let's substitute the value of the original area into this equation. We know that the original area is 13 m^2. Since the area of the triangle is equal to (original base * original height) / 2, we can solve for the original base and height:
13 = (original base * original height) / 2
26 = original base * original height
Since we only know the area, we can assume any two numbers that when multiplied together equal 26. For example, we can assume the original base to be 2 and the original height to be 13, or vice versa.
Now, substitute 26 for (original base * original height) in the equation for the new area:
New Area = (3 * 2) * (3 * 13) / 2
New Area = 6 * 39 / 2
New Area = 234 / 2
New Area = 117 m^2
So, the correct answer choice is C. 117 m^2.
Yes, you are right! The area of the new triangle is 117 m^2.