Question

A right triangle has an area of 24 ft². The dimensions of the triangle are increased by a scale factor of 6. What is the area of the new triangle?
A. 48 ft²

B. 72 ft²

C. 144 ft²

D. 60 ft²

Answer 1

Answer: The area of the new triangle is $864\ ft^2$

Step-by-step explanation:

For this exercise it is important to remember that, when you increase the dimensions of a triangle by a scale factor of $k$ ,he area of the triangle is increased by a factor $k^2$.

In this case, you know that the area of the right triangle is $24\ ft^2$.  

Since the dimensions of the right triangle are increased by a scale factor of 6, then you must multiply the original area by a factor of $6^2$.

Therefore, the area of the new triangle is:

$A'=(24\ ft^2)(6^2)\\\\A'=(24\ ft^2)(36)\\\\A'=864\ ft^2$

Answer 2

Answer:

Area of new triangle must be 864 $ft^2$

Step-by-step explanation:

Given:

Area of right angle triangle = 24 $ft^2$

Dimension of the triangle is increased by scale factor of 6.  

To Find:

Area of new triangle=?

Solution:

Lets say perpendicular side which is height of right angled triangle = a

And base of right angled triangle be represented by b  

Area of triangle =$\frac{1}{2}base \times height$

Area of triangle=$\frac{1}{2}( a\times b )$

substituting the given values,

=> $\frac{1}{2} ( a \times b ) = 24$

=> ab = 24 x 2 = 48  

=> ab = 48    -------(1)

Now given that Dimension of triangle is increased by scale factor of 6 means dimension of new triangle is equal to 6 times dimension of first triangle

=>perpendicular side which is Height of new right angled triangle  = 6 x a = 6a

And base of new right angled triangle = 6 x b = 6b

Area of new triangle =$\frac{1}{2}base\times height= \frac{1}{2} (6a \times 6b )$

Area of new triangle = 18ab

Substituting value of ab as 48 from eq (1) in above equation we get

Area of new triangle = 18 x 48 = 864