Find The Indicated Length Geometry

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The rectangle beneath has a perimeter of 54. Detect the lengths of the unknown side. That is, find Due south.

Rectangle_7-20

Explanation:

For a rectangle, its perimeter is the sum of all for sides. We tin write

54=20+20+S+S

Simplify

54=40+2S

Solve for Due south

14=2S

S=7

Given a rectangle with a length units longer than its width and an area of square units, find the length of the rectangle'southward shortest side.

Right answer:

Explanation:

The given rectangle has a length that is units longer than its width. This can be expressed in the following equation, where is the length and is the width of the rectangle.

l = w +10

Since the surface area of the rectangle is equal to its length multiplied by its width ( A = l * w ), and the surface area of the rectangle is given, the following equation must exist truthful.

75 = l * w

Replacing in this equation with its value stated in the first equation results in the following.

75 = (w+10) * w

Distribute the variable into the parentheses.

75 = w^2 +10w

w^2 +10w -75 = 0

Cistron the polynomial.

(w-5)(w+15) = 0

and are both solutions for this equation, only is not valid as a width for a rectangle. The width of the rectangle is units, which is the shorter side since the length is units longer (l = w+10) .

There is a regtangular fence surrounding a park. The perimeter of the argue is . What is the width of the fence if the length is ?

Correct answer:

A rectangle has a perimiter of 36 inches and a length of 12 inches. What is the width of the rectangle in inches?

Correct answer:

Explanation:

To find the width, multiply the length that you lot have been given by 2, and subtract the effect from the perimeter. You now have the total length for the remaining two sides. This number divided by two is the width.

$36-(12\cdot 2)=12$

12/2=6

A rectangle four and a half times as long every bit it is broad has perimeter of 272 centimeters. To the nearest 10th of a centimeter, how wide is it?

Right reply:

$24.7\ cm$

Explanation:

If we call the width of this rectangle , and then its length can be restated every bit $L=4\frac{1}{2}w$ , or, equivalently, L=4.5w .

The perimeter can then be written equally:

P=2L+2w=2(4.5w)+2w

Since the perimeter of the rectangle is 272 cm, we can ready the following equation:

2(4.5w)+2w=272

9w+2w=272

11w=272

$w=\frac{272}{11}=24.7$

The width, in cm, of a rectangular fence is 2 more than half its length, in cm. Which of the following gives the width, w cm, in terms of length, fifty cm, of the rectangular fence?

Possible Answers:

west = ½ l + 2

w = 2l + two

w = 2l – 2

w = ½ l – 2

Correct reply:

w = ½ l + 2

Caption:

To find the width, we must take half of the length, which ways we must separate the length by 2. And then nosotros must accept 2 more than that number, which ways we must add 2 to the number. Combining these, nosotros get:

w = ½ 50 + 2

The width of a rectangle is 2 inches longer than three times its length. Which of the following equations gives the width, w, of the rectangle in terms of its length, l,?

Possible Answers:

w = 3l + 2

w = 3l – 2

w = 1/3l +2

west = 6l +two

Correct reply:

w = 3l + two

Explanation:

The width equals 3 times the length, and so 3l, plus an additional two inches, so + 2, = 3l + 2

Your dad shows y'all a rectangular scale cartoon of your house. The drawing is 6 inches by 8 inches. You're trying to figure out the actual length of the shorter side of the house. If you know the actual length of the longer side is 64 feet, what is the actual length of the shorter side of the firm (in anxiety)?

Explanation:

We tin can solve this by setting up a proportion and solving for 10,the length of the shorter side of the house. If the cartoon is scale and is 6 : eight, then the bodily business firm is 10 : 64. Then we tin cantankerous multiply and so that 384 = eight10. Nosotros then divide by 8 to get x = 48.

If the perimeter of a rectangle is and the length of the rectangle is, what is the width of the rectangle?

Correct answer:

Caption:

Recall how to discover the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can then manipulate this equation to find the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to find the width.

$\text{width}=\frac{14}{2}-5=7-5=2$

If the perimeter of a rectangle is and the length of the rectangle is, what is the width of the rectangle?

Right answer:

Explanation:

Recall how to discover the perimeter of a rectangle.

$\text{Perimeter}=2(\text{length}+\text{width})$

We can and so dispense this equation to discover the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Now, plug in the information given by the question to notice the width.

$\text{width}=\frac{18}{2}-3=9-3=6$

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