MATH SOLVE

3 months ago

Q:
# o perímetro de um retângulo é 14cm. um dos lados mede 4 cm. determine a diagonal do retângulo

Accepted Solution

A:

Answer:The diagonal of the rectangle is [tex]5\ cm[/tex]Step-by-step explanation:The question In EnglishThe perimeter of a rectangle is 14cm. one side measures 4cm. determine the diagonal of the rectangle.Letx-----> the length of the rectangley----> the width of the rectanglewe know thatThe 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 Awe have that[tex]x=4\ cm[/tex]Find the value of ysubstitute in the equation A[tex]7=(4+y)[/tex][tex]y=7-4=3\ cm[/tex]Find the diagonal of the rectangleApplying 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]