Question

Martin is dilating a blue triangle to create a yellow triangle. If he used a scale factor of

Answer 1

Answer:

See Explanation

Step-by-step explanation:

The question has missing details, as the scale factor is not given. However, I will give a general explanation on how to calculate the area and perimeter of a dilated shape (triangle).

The following assumptions, apply:

(1) Scale factor of 1/2 from the blue to the yellow triangle.

(2) The dimension of the blue triangle are:

$Base = x$

$Sides= y\ and\ z$

$Height= h$

First, calculate the dimensions of the yellow triangle.

The dimension will be the product of the scale factor and the dimensions of the blue triangle.

So, we have:

$Base = \frac{1}{2} * x = \frac{1}{2}x$

$Sides = \frac{1}{2}y\ and\ \frac{1}{2}z$

$Height = \frac{1}{2}h$

The perimeter of the blue triangle is:

$P_1 =Base + Sides$

$P_1 = x + y + z$

The perimeter of the yellow triangle is:

$P_2 =Base + Sides$

$P_2 = \frac{1}{2}x + \frac{1}{2}y + \frac{1}{2}z$

Factorize

$P_2 = \frac{1}{2}[x + y + z]$

Recall that: $P_1 = x + y + z$

So:

$P_2 = \frac{1}{2}*P_1$

This implies that the perimeter of the yellow triangle is a product of the scale factor and the perimeter of the blue triangle.

The area of the blue triangle is:

$A_1 = \frac{1}{2}* Base * Height$

$A_1 = \frac{1}{2} * x* h$

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

The area of the yellow triangle is:

$A_2 = \frac{1}{2} * Base * Height$

$A_2 = \frac{1}{2}* (\frac{1}{2}x) * (\frac{1}{2}h)$

Rewrite as:

$A_2 = \frac{1}{2}* \frac{1}{2} [\frac{1}{2}x h]$

$A_2 = (\frac{1}{2})^2 *[\frac{1}{2}x h]$

Recall that:$A_1 = \frac{1}{2} xh$

So:

$A_2 = (\frac{1}{2})^2 *A_1$

This implies that the area of the yellow triangle is a product of the square of the scale factor and the area of the blue triangle.