contestada

A square and a rectangle have the same perimeter. The square has a side length of 8x units. The rectangle has a length of (5x+8) units and a width of 14 units. What will the perimeter of both the rectangle and the square

Respuesta :

calculista

Answer:

The perimeter of both figures is equal to [tex]64\ units[/tex]

Step-by-step explanation:

step 1

we know that

The perimeter of a square is equal to

[tex]P=4b[/tex]

where

b is the side length of the square

we have

[tex]b=8x\ units[/tex]

substitute

[tex]P=4(8x)=32x\ units[/tex]

step 2

we know that

The perimeter of a rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=(5x+8)\ units[/tex]

[tex]W=(14)\ units[/tex]

substitute

[tex]P=2(5x+8+14)=10x+44\ units[/tex]

step 3

Equate both perimeters and solve for x

[tex]10x+44=32x[/tex]

[tex]32x-10x=44[/tex]

[tex]22x=44[/tex]

[tex]x=2\ units[/tex]

step 4

Find the perimeter of both

square

[tex]P=32x=32(2)=64\ units[/tex]

rectangle

[tex]P=10x+44=10(2)+44=64\ units[/tex]