Answer:
Perimeter = 34 cm
Area = 60 [tex]cm^{2}[/tex]
Step-by-step explanation:
The equation to find the perimeter of a rectangle is:
P = 2(l + w)
l = length
w = width
To find the length we have to use Pythagorean Theorem:
[tex]a^{2} + b^{2} = c^{2}[/tex]
a = 12 cm
b = ?
c = 13 cm
Plug in and solve for b:
[tex](12^{2})+b^{2} = (13^{2})[/tex]
[tex]144 + b^{2} = 169[/tex] Distribute the squares
[tex]b^{2} = 25[/tex] Subtract 144 from 169
[tex]\sqrt{b^{2} } =\sqrt{25}[/tex] Square root both sides
b = 5 cm
Now that we have found the length, and we know the width, we can find the perimeter:
P = 2(12 + 5) = 2(17) = 34
The perimeter of the rectangle is 34 cm.
To find the area use this equation:
A = lw
Plug in the values for length and width and solve:
A = (5 cm)(12 cm)
A = 60 [tex]cm^{2}[/tex]
The area of the rectangle is 60 [tex]cm^{2}[/tex].
Hope this helps!!
