the perimeter of a rectangle is 124 cm. the length is six more than three times the width. what are the dimensions of the rectan

Question

viva [34]

4 years ago

11

the perimeter of a rectangle is 124 cm. the length is six more than three times the width. what are the dimensions of the rectan

gle?

Mathematics

2 answers:

just olya [345] · Answer 1 · 2021-11-24T07:13:26+03:00

just olya [345]4 years ago

5 0

P = 2(L + W)
P = 124
L = 3W + 6

124 = 2(3W + 6 + W)
124 = 2(4W + 6)
124 = 8W + 12
124 - 12 = 8W
112 = 8W
112/8 = W
14 = W <=== width is 14 cm

L = 3W + 6
L = 3(14) + 6
L = 42 + 6
L = 48 <=== length is 48 cm

RideAnS [48] · Answer 2 · 2021-11-24T08:15:54+03:00

Our first task in this problem is to set up variables that represent length and width.

<u>Let's first identify our values:</u>

X → Width

3x + 6 → Length

Before moving on, it's always a great idea to draw a picture of the rectangle to visualize what's going on. I will provide a picture.

Now, we can use the first sentence of the problem to set up our equation.

The perimeter of a rectangle is the distance around the outside of the figure. If our perimeter is 124 cm, we can set up an equation to represent this.

<h3>x + x + 3x + 6 + 3x + 6 = 124cm.</h3><h3 /><h3>If we simplify on the left side we will get </h3>

<h3>8x + 12 = 124</h3><h3> -12 -12</h3><h3 /><h2>8x = 112</h2><h2>÷8 ÷8</h2><h2 /><h2>X = 14</h2><h2 /><h2>Width = 11 cm</h2><h2>Length = 48 cm</h2>