Question

In the figure, triangle CAE is an enlargement of triangle CBD with scale factor of 4/3. The area of the smaller triangle is 9cm2. What is the area of the bigger traingle

Answer 1

16 cm^2

Explanation:

Given

`\triangle CAE` -- Bigger Triangle

`\triangle CBD` -- Smaller Triangle

`k = (4)/(3)` --- Scale factor

Area of CBD = 9

Required

Determine the area of CAE

The area of triangle CBD is:

`A_1 = (1)/(2)bh`

`(1)/(2)bh = 9`

The area of CAE is:

`A_2 = (1)/(2)BH`

Where:

`B = (4)/(3)b` and

`H = (4)/(3)h`

The above values is the dimension of the larger triangle (after dilation).

So, we have:

`A_2 = (1)/(2)*(4)/(3)b * (4)/(3) * h`

`A_2 = (1)/(2)*(4)/(3) * (4)/(3) *b* h`

`A_2 = (1)/(2)*(16)/(9) *b* h`

Re-order

`A_2 = (16)/(9)*(1)/(2)* b* h`

`A_2 = (16)/(9)*(1)/(2)bh`

Recall that:

`(1)/(2)bh = 9`

`A_2 = (16)/(9)*9`

`A_2 = 16`

Hence, the area is 16 cm^2