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Leona [35]
3 years ago
14

Your parents decide they would like to install a rectangular swimming pool in the backyard. There is a 15-foot by 20-foot rectan

gular area available. Your parents request a 3-foot edge around each side of the pool. Draw a diagram of this situation in a coordinate plane. What is the perimeter and area of the largest swimming pool that will fit?

Mathematics
1 answer:
Lilit [14]3 years ago
5 0

Answer:

  • perimeter: 46 ft
  • area: 126 ft²

Step-by-step explanation:

Since the 3 ft edge is on both sides of the pool, each dimension of the pool is 6 ft shorter than the corresponding dimension of the space. The pool will be 15 ft -6 ft = 9 ft in one direction and 20 ft -6 ft = 14 ft in the other direction.

The perimeter of the pool is the sum of its side lengths:

  P = 9 ft + 14 ft + 9 ft + 14 ft = 2(9 ft +14 ft) = 2(23 ft)

  P = 46 ft

__

The area of the pool is the product of its length and width:

  A = (14 ft)(9 ft) = 126 ft²

The perimeter and area are 46 ft and 126 ft², respectively.

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I need help asap pls and thank you ;)
olga55 [171]

Answer:

\text{Length of AB is }\frac{ah}{a+h}

Step-by-step explanation:

Given △KMN, ABCD is a square where KN=a, MP⊥KN, MP=h.

we have to find the length of AB.

Let the side of square i.e AB is x units.

As ADCB is a square ⇒ ∠CDN=90°⇒∠CDP=90°

⇒ CP||MP||AB

In ΔMNP and ΔCND

∠NCD=∠NMP     (∵ corresponding angles)

∠NDC=∠NPM     (∵ corresponding angles)

By AA similarity rule,  ΔMNP~ΔCND

Also, ΔKAP~ΔKPM by similarity rule as above.

Hence, corresponding sides are in proportion

\frac{ND}{NP}=\frac{CD}{MP} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{AB}{PM} \\\\\frac{ND}{NP}=\frac{x}{h} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{x}{h}\\\\\frac{NP}{ND}=\frac{h}{x} \thinspace\thinspace and\thinspace\thinspace \frac{KP}{KA}=\frac{h}{x}\\\\\frac{PD}{ND}=\frac{h}{x}-1 \thinspace\thinspace and\thinspace\thinspace \frac{AP}{KA}=\frac{h}{x}-1\\

KA(\frac{h}{x}-1)=AP

ND(\frac{h}{x}-1)=PD

Adding above two, we get

(KA+ND)(\frac{h}{x}-1)=(AP+PD)

⇒ (KN-AD)=\frac{x}{(\frac{h}{x}-1)}

⇒ a-x=\frac{x}{(\frac{h}{x}-1)}

⇒ a-x=\frac{x^2}{h-x}

⇒ x^2=ah-ax-xh+x^2

⇒ x(h+a)=ah

⇒ x=\frac{ah}{a+h}

3 0
3 years ago
What is the base of a triangle that has a height of 6 centimeters and an area of 18 centimeters? Use the formula , where A repre
harina [27]

Answer:

The base of the triangle is 6cm.

Step-by-step explanation:

The find the base of a triangle, use this formula.

Formula : 1/2 x b x h

<em>If you would like some more explanation, see the attached image.</em>

5 0
3 years ago
Jaime wrote 4.4_0.33=1.1 is his answer reasonable?why're why not?
shusha [124]
No you have to make sure to line up the decimals when subtracting them. Do not just line of the numbers, this wills get you the wrong answers. Hope this helps. If you need anything else just call for a helping hand.

7 0
3 years ago
What is the slope of the line that passes through the points (4, 6) and<br> (-16, -18)?
storchak [24]

Answer:

-3 / 5

Step-by-step explanation:

18-6 / -16-4

12 / -16-4

12 / -20

-3 / 5

3 0
3 years ago
PLS HELP ASAP WILL MARK BRAINLIEST
Lady_Fox [76]
Yes he will



Because math is cool
3 0
3 years ago
Read 2 more answers
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