Question

On a math test, the students are asked to

find the perimeter of rectangle STUV with
vertices S(-6.5, -8.5), T(2.5, -8.5),
U(2.5, 3.5), and V-6.5, 3.5). Alberto writes
that the perimeter of the rectangle is
18 units. Is he correct? Explain.

Answer 1

Alberto is incorrect. Perimeter is 42 units.

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.