Answer:
The diagonal of the rectangle is [tex]5\ cm[/tex]
Step-by-step explanation:
The question In English
The perimeter of a rectangle is 14cm. one side measures 4cm. determine the diagonal of the rectangle.
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(x+y)[/tex]
[tex]P=14\ cm[/tex]
so
[tex]14=2(x+y)[/tex]
[tex]7=(x+y)[/tex] -----> equation A
we have that
[tex]x=4\ cm[/tex]
Find the value of y
substitute in the equation A
[tex]7=(4+y)[/tex]
[tex]y=7-4=3\ cm[/tex]
Find the diagonal of the rectangle
Applying the Pythagoras Theorem
[tex]d=\sqrt{x^{2}+y^{2}}[/tex]
[tex]d=\sqrt{4^{2}+3^{2}}[/tex]
[tex]d=\sqrt{25}\ cm[/tex]
[tex]d=5\ cm[/tex]
