Question

O perímetro de um retângulo é 14cm. um dos lados mede 4 cm. determine a diagonal do retângulo

Answer 1

The diagonal of the rectangle is
`5\ cm`

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

`P=2(x+y)`

`P=14\ cm`

so

`14=2(x+y)`

`7=(x+y)` -----> equation A

we have that

`x=4\ cm`

Find the value of y

substitute in the equation A

`7=(4+y)`

`y=7-4=3\ cm`

Find the diagonal of the rectangle

Applying the Pythagoras Theorem

`d=\sqrt{x^(2)+y^(2)}`

`d=\sqrt{4^(2)+3^(2)}`

`d=√(25)\ cm`

`d=5\ cm`