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

Answer:

16 cm^2

Step-by-step explanation:

Given

$\triangle CAE$ -- Bigger Triangle

$\triangle CBD$ -- Smaller Triangle

$k = \frac{4}{3}$ --- Scale factor

Area of CBD = 9

Required

Determine the area of CAE

The area of triangle CBD is:

$A_1 = \frac{1}{2}bh$

$\frac{1}{2}bh = 9$

The area of CAE is:

$A_2 = \frac{1}{2}BH$

Where:

$B = \frac{4}{3}b$ and

$H = \frac{4}{3}h$

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

So, we have:

$A_2 = \frac{1}{2}*\frac{4}{3}b * \frac{4}{3} * h$

$A_2 = \frac{1}{2}*\frac{4}{3} * \frac{4}{3} *b* h$

$A_2 = \frac{1}{2}*\frac{16}{9} *b* h$

Re-order

$A_2 = \frac{16}{9}*\frac{1}{2}* b* h$

$A_2 = \frac{16}{9}*\frac{1}{2}bh$

Recall that:

$\frac{1}{2}bh = 9$

$A_2 = \frac{16}{9}*9$

$A_2 = 16$

Hence, the area is 16 cm^2