Question

A triangle with an area of 2/3 cm? is dilated by a factor of 6. What is the area of the dilated triangle? Enter your answer in the box. Do not leave your answer as a fraction.

Answer 1

Let A be the area of the dilated triangle.

Given the statement: A triangle with an area of 2/3 cm2 is dilated by a factor of 6.

⇒ Pre-image triangle has an area =
`(2)/(3)`
`cm^2`

Scale factor(k) states that the dimension of the Dilated-image is 6 times longer than the dimensions of the pre-image.

i.e,

`k = \frac{\text{Dilation image}}{\text{Pre-image}}`

Substitute the given values to find the value of area of dilated triangle.

`6 = (A)/((2)/(3) )`

or

`6 = (3A)/(2)`

Multiply both sides by 2 we get;

`12 = 3A`

Divide both sides by 3 we get;

`4 = A`

Therefore, the area of the dilated triangle is,
`4 cm^2`