Answer:
Part 1) The perimeter is [tex]P=6\sqrt{6}\ cm[/tex]
Part 2) The diagonal is [tex]d=\sqrt{30}\ cm[/tex]
Step-by-step explanation:
The question in English is
You have a rectangle whose base is twice the height and its area is 12
square centimeters. Calculate the perimeter of the rectangle and its diagonal
step 1
Find the dimensions of rectangle
we know that
The area of rectangle is equal to
[tex]A=bh[/tex]
[tex]A=12\ cm^2[/tex]
so
[tex]bh=12[/tex] ----> equation A
The base is twice the height
so
[tex]b=2h[/tex] ----> equation B
substitute equation B in equation A
[tex](2h)h=12\\2h^2=12\\h^2=6\\h=\sqrt{6}\ cm[/tex]
Find the value of b
[tex]b=2\sqrt{6}\ cm[/tex]
step 2
Find the perimeter of rectangle
The perimeter is given by
[tex]P=2(b+h)[/tex]
substitute
[tex]P=2(2\sqrt{6}+\sqrt{6})\\P=6\sqrt{6}\ cm[/tex]
step 3
Find the diagonal of rectangle
Applying the Pythagorean Theorem
[tex]d^2=b^2+h^2[/tex]
substitute
[tex]d^2=(2\sqrt{6})^2+(\sqrt{6})^2[/tex]
[tex]d^2=30[/tex]
[tex]d=\sqrt{30}\ cm[/tex]
