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

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

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 =
`(1)/(2)base * height`

Area of triangle=
`(1)/(2)( a* b )`

substituting the given values,

=>
`(1)/(2) ( a * 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 =
`(1)/(2)base* height= (1)/(2) (6a * 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

Answer 2

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

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`