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- Let y represent the width of a rectangle and let x represent the rectangle's lengu.
length of the rectangle is three less than four times its width and the perimeter is
54 centimeters.
Write a system of equations and solve them to find the dimensions of the rectangle.

Respuesta :

ridxee

Answer:

Length: 21 cm and Width:  6cm

Step-by-step explanation:

Let [tex]y[/tex] be the width and [tex]x[/tex] length of the rectangle. We know:

[tex]x = 4y -3[/tex] -------- eq. 1

[tex]54 = 2x + 2y[/tex]    (Perimeter of the rectangle) ------- eq.  2

Substitute equation 1 in equation 2:

[tex]54 = 2(4y-3) + 2y\\54 = 8y - 6 + 2y\\54 + 6 = 8y + 2y\\60 = 10 y\\\\\frac{60}{10}= y\\y = 6[/tex]

Using the value of y, we find x.

[tex]x = 4y - 3\\x = 4(6) -3\\x= 24 - 3\\x = 21[/tex]

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