Question

Se tiene un rectángulo cuya base mide el doble que su altura y su área es 12

centímetros cuadrados. Calcular el perímetro del rectángulo y su diagonal.

Answer 1

Part 1) The perimeter is
`P=6√(6)\ cm`

Part 2) The diagonal is
`d=√(30)\ cm`

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

`A=bh`

`A=12\ cm^2`

so

`bh=12` ----> equation A

The base is twice the height

so

`b=2h` ----> equation B

substitute equation B in equation A

`(2h)h=12\\2h^2=12\\h^2=6\\h=√(6)\ cm`

Find the value of b

`b=2√(6)\ cm`

step 2

Find the perimeter of rectangle

The perimeter is given by

`P=2(b+h)`

substitute

`P=2(2√(6)+√(6))\\P=6√(6)\ cm`

step 3

Find the diagonal of rectangle

Applying the Pythagorean Theorem

`d^2=b^2+h^2`

substitute

`d^2=(2√(6))^2+(√(6))^2`

`d^2=30`

`d=√(30)\ cm`