Question

1.The area of a given rectangle is 5z^3-80z and its length is 5z^2+ 20z.Find its length
2.The area if a given rectangle is 5p^2-25p+20 and its length is p-1.Find its breadth
3.The area of a given square is 49y^2 + 84yz +36z^2.Find its perimeter
PLZ EXPLAIN ME THIS WITH ALL THE STEPS AND NICE EXPLANATION.URGENT

Answer 1

Answer:

(1) z - 4

(2) 5p - 20

(3) 28y + 24z

Step-by-step explanation:

(1)

Area = 5z³ - 80z.

Length = 5z² + 20z.

We know that Area of rectangle = Length * Breadth

⇒ 5z³ - 80z = (5z² + 20z) * B

⇒ B = (5z³ - 80z)/(5z² + 20z)

⇒ B = z - 4(5z² + 20z)/(5z² + 20z)

⇒ B = z - 4.

Therefore, breadth = z - 4.

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(2)

Given Area = 5p² - 25p + 20.

Given,Length = p - 1.

Area = Length * breadth

⇒ 5p² - 25p + 20 = (p - 1) * B

⇒ B = 5(p² - 5p + 4)/(p - 1)

⇒ B = 5(p² - p - 4p + 4)/(p - 1)

⇒ B = 5(p(p - 1) - 4(p - 1))/(p - 1)

⇒ B = 5(p - 4)(p - 1)/(p - 1)

⇒ B = 5(p - 4)

⇒ B = 5p - 20.

Therefore, breadth = 5p - 20.

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(3)

Area of square = 49y² + 84yz + 36z².

⇒ (7y + 6z)².

We know that Area of square = (s)^2

⇒ (7y + 6z)² = (s)²

⇒ s = 7y + 6z.

We know that perimeter of square = 4s

⇒ 4(7y + 6z)

⇒ 28y + 24z.

Hope it helps!

Answer 2

1.

Given: Area of the rectangle is 5z^3 - 80z and its length is 5z^2 + 20z.

To find: Its breadth.

Answer:

Formula to find area = length*breadth

Breadth = Area/length

Let the breadth be x.

Substituting the given values:

5z^3 - 80z = 5z^2 + 20z*x

x = 5z^3 - 80z/5z^2 + 20 - z

Since 5z in common in both the numerator and denominator,

x = 5z*(z^2 - 16)/5z*(z + 4)

x = 5z*(z + 4)(z - 4)/5z*(z + 4)

x = z - 4

Therefore the breadth is z - 4.

2.

Given: Area of a rectangle is 5p^2 - 25p + 20 and its length is p - 1.

To find: Its breadth.

Answer:

Formula to find area of a rectangle = length*breadth

Breadth = Area/length

Let the breadth be x.

Substituting the given values:

x = 5p^2 - 25p + 20/p - 1

Using "Splitting the middle term" method,

Sum = -25

Product = 100

The options are: 100 and 1, 50 and 2, 10 and 10 and 20 and 5.

-20 and -5 (Sum = -20 + -5 = -25, Product = -20*-5 = 100)

x = (p - 20)*(p - 5)/(p - 1)

Therefore the breadth is (p - 20)*(p - 5)/(p - 1).

3.

Given: Area of a square is 49y^2 + 84yz + 36z^2.

To find: Its perimeter.

Answer:

Formula to find area of a square = Side*Side = Side^2

Formula to find the side = √Side

According to the identities, (y + z)^2 = y^2 + 2yz + z^2.

(7y + 6z)^2 = 49y^2 + 84yz + 36z^2

Therefore side = √(7y + 6z)^2 = 7y + 6z.

Perimeter = 4*Side

Perimeter = 4(7y + 6z) = 28y + 24z.

Hope it helps :)