What is the solution of the system of linear equations below?

A rectangle pool is 7 ft wide, it is 3 times as long as it is wide what’s the dimensions of the pool?

svetoff [14.1K]

The length is 3 times longer than the width (7)

3 x 7 = 21

the length is 21.

To find perimeter, add all sides together:

21 + 21 + 7 + 7 = 42 + 14 = 56

56 ft is your answer

hope this helps

3 0

2 years ago

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The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased

White raven [17]

Statement:

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

To find out:

The length of the larger side of the right angled triangle.

Solution:

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = $\frac {(52 - 6y)}{4}$ ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, $\frac {(2704-624y +36y²)}{16}$ + y² = 52

or, $\frac {(2704-624y +36y² + 16y²)}{16}$ = 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

Answer:

6 cm

Hope you could understand.

If you have any query, feel free to ask.

6 0

2 years ago

Segment BDSegment BD is a perpendicular bisector of segment ACsegment AC . AD=8x−15AD=8x−15 and DC=57DC=57 .

Charra [1.4K]

I hope this helps you

7 0

2 years ago

Read 2 more answers

In 2014, there were 16,400 students at College A, with a projected enrollment increase of 640 students per year. In the same yea

zhenek [66]

Answer:

4 Years

Step-by-step explanation:

I just continually added the numbers til' I got 18,960 on Both Colleges.

8 0

2 years ago

the length of a new rectangle playing field is 6 yards longer than quadruple the width. if the perimeter of the rectangle plaing

Vika [28.1K]

The length and width of a new rectangle playing field are 214 yards and 52 yards respectively.

<h3>What is the area of the rectangle?</h3>

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have:

The length of a new rectangle playing field is 6 yards longer than quadruple the width.

Let's suppose the length is l and width is w of a rectangle:

From the problem:

l = 6 + 4w

Perimeter P = 2(l + w)

532 = 2(l + w)

Plug l = 6+4w in the above equation:

532 = 2(6 + 4w + w)

266 = 6 + 5w

260 = 5w

w = 52 yards

l = 6 +4(52) = 214 yards

Thus, the length and width of a new rectangle playing field are 214 yards and 52 yards respectively.

Learn more about the area of rectangle here:

brainly.com/question/15019502

#SPJ1

5 0

1 year ago