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?
2 answers:
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>
You might be interested in
a. Length of the fence around the field = perimeter of quarter circle = 892.7 ft.
b. The area of the outfield is about 39,584 sq. ft..
<h3>What is the Perimeter of a Quarter Circle?</h3>Perimeter of circle = 2πr
Perimeter of a quarter circle = 2r + 1/4(2πr).
a. The length of the fence around the field = perimeter of the quarter circle fence
= 2r + 1/4(2πr).
r = 250 ft
Plug in the value
The length of the fence around the field = 2(250) + 1/4(2 × π × 250)
= 892.7 ft.
b. Size of the outfield = area of the full field (quarter circle) - area of the infield (cicle)
= 1/4(πR²) - πr²
R = radius of the full field = 250 ft
r = radius of the infield = 110/2 = 55 ft
Plug in the values
Size of the outfield = 1/4(π × 250²) - π × 55²
= 49,087 - 9,503
= 39,584 sq. ft.
Learn more about perimeter of quarter circle on:
