Mathematics High School

the perimeter of a rectangle is 20 cm and it's area is 24cm^2 find the length and breath of the rectangle

Answers

Answer 1

Answer:

length = 6cm , breadth = 4cm

Step-by-step explanation:

Let's assume length = l

breadth = b

Given perimeter of a rectangle = 20 cm

2(l+b) = 20

l+b = 20/2

l+b = 10

l = 10 - b____(1)

Given area of rectangle = 24 cm²

l×b = 24____(2)

(1) in (2) => l × b = 24

(10-b) × b = 24

10b - b² = 24

10b = 24 + b²

0 = b² - 10b + 24

b² - 10b + 24 = 0

b² + 6b + 4b + 24 = 0

b(b+6) +4(b+6) = 0

(b+4)(b+6) = 0

b+4 = 0. &. b+6 = 0

b = -4. b = -6

breadth must be less than length and it should be positive

So b = 4 cm

b=4 in (1)

(1)=> l = 10 - b

l = 10 - 4

l = 6

Related Questions

Factorise 2x^2 + x - 6

Answers

[tex] \rm \: {2x}^{2} + x - 6[/tex]

[tex] \rm \: {2x}^{2} + 4x - 3x - 6[/tex]

[tex] \rm \: {2x} \times (x + 2)- 3x \times (x + 2)[/tex]

[tex] \rm \: (x + 2) \times (2x - 3)[/tex]

In circle O, ST is a diameter.

Circle O is shown. Line segment S T is a diameter. Line segments R O and U O are radii. Angles R O U and U O T are congruent. The measure of arc R S is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.

What must be the value of x?

22.0
25.0
25.4
37.2

Answers

The value of x must be 25.0. The correct option is the second option- 25.0

Solving Linear equations

From the question, we are to determine the value of x

From the given diagram, we can write that

m ∠SOR + m ∠UOR + m ∠TOU = 180° (Sum of angles on a straight line)

∴ (2x +8)° + (3x - 14)° + (3x -14)° = 180°

2x° + 8° + 3x° -14° + 3x° -14° = 180°

Collect like terms

2x° + 3x° + 3x° + 8° - 14° -14° = 180°

8x° -20° = 180°

8x° = 180° + 20°

8x° = 200°

x = 200/8

x = 25.0

Hence, the value of x must be 25.0. The correct option is the second option- 25.0

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Answer:

25.0

Step-by-step explanation:

just took it

Which classification describes the following system of equations? inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent.

Answers

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

[tex]\rm x=y+z[/tex]

Plug this value in the equation (2) and (3):

[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

Learn more about the linear equation here:

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What is the difference of a surface area and a volume

Answers

Surface area is all the area of all sides while volume is the amount of space (a substance) occupies in a solid.

For example:

A cube has a length,breadth and height of 5cm,find:

a) surface area of the cube;

b) and the volume of the cube.

a) area of one side of the cube = 5 x 5

= 25cm²

Total surface area = 25cm x 6 (a cube has 6 sides)

= 150cm²

b) volume of cube = length x breadth x height

= 5 x 5 x 5

= 125cm³

Hope this helps you :]

p.s. can you mark me as the brainliest? <3

An unusual number cube (with 6 sides) has the numbers 2, 2, 4, 4, 6, and 6 on its faces.
It is rolled once. Match the outcome to its probability.
1. P(2 or 4)
2. A(multiple of 2)
3. P(multiple of 3)
4. P(odd prime numbers)

2/3
0
1
1/3

Answers

Answer:

1. P(2 or 4) - 2/3

2. P(multiple of 2) - 1

3. P(multiple of 3) 1/3

4. P(odd prime numbers) 0

Step-by-step explanation:

Good luck lol

P(2 or 4) = 2/3

P( multiple of 2) = 1

P( multiple of 3) = 1/3

P(odd prime numbers) = 0

What is probability?

Probability is the likelihood of an event happening or not.

Analysis:

possible outcome = (2,2,4,4,6,6) = 6

P(2 or 4)

n( 2) = required outcome = (2,2) = 2

P(2) = 2/6 = 1/3

n(4) = (4,4) = 2

P(4) = 2/6 = 1/3

P(2 or 4) = 1/3 + 1/3 = 2/3

n( multiple of 2) = (2,2,4,4,6,6) = 6

P( multiple of 2) = 6/6 = 1

n(multiple of 3) = (6,6) = 2

P(multiple of 3) = 2/6 = 1/3

P(odd prime numbers) = 0

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A major arc will have a measure that is
O A. greater than 180°
OB. less than 180°
O C. equal to 180°

Answers

Think Major greater than 180°, Minor less than 180°. If arc equals 180° than it is a semi circle.

A.

Help my semester ends in 17 hours
i'm so confused this is all they put

Apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in real
world and mathematical problems in two and
three dimensions

Answers

Find the lengths of the sides. Determine how long a right triangle side lengths are.

HELP MEE ,20 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r

Answers

Celina says true that each of the following expressions is actually a binomial expression.

What is binomial?

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

Celina says that each of the following expressions is actually a binomial in disguise:

a. 5abc - 2a² + 6abc = 11abc - 2a²