Question

On a math test, the students are asked to

Answer 1

Answer:

Alberto is incorrect. Perimeter is 42 units.

Step-by-step explanation:

Given:

The vertices of the triangle are $S(-6.5, -8.5), T(2.5, -8.5),U(2.5, 3.5), \textrm{ and } V(-6.5, 3.5).$

Perimeter of a triangle of length $l$ and width $b$ is given as:

$P=2(l+b)$

Here, $l=ST,b=TU$

Distance between two points $A(x_{1},y_{1})$ and $B(x_{1},y_{2})$ is given as:

$AB=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

So, the length ST is,

$l=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\l=\sqrt{(2.5-(-6.5))^{2}+(-8.5-(-8.5))^{2}}\\l=\sqrt{9^{2}+0}=9$

Width TU is,

$b=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\b=\sqrt{(2.5-2.5))^{2}+(3.5-(-8.5))^{2}}\\b=\sqrt{0+12^{2}}=12$

Therefore, the perimeter is given as:

Perimeter = $2(l+b)=2(9+12)=2(21)=42$ units.

Hence, the perimeter written by Alberto is incorrect as perimeter is not 18 units bu 42 units.