Question

Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of K, where k > 0. ( Answer Part A, Answer Part B, and Answer Part C. ( Will Mark Brainliest and do not repaste another students answer on Brainly or any other website or you'll be reported. Thank you. ​

Answer 1

$\bold{\huge{\underline{\pink{ Solution }}}}$

Given :-

• Rectangle 1 has length x and width y
• Rectangle 2 is made by multiplying each dimensions of rectangle 1 by a factor of k
• Where, k > 0

Answer 1 :-

Yes, The rectangle 1 and rectangle 2 are similar .

According to the similarity theorem :-

• If the ratio of length and breath of both the triangles are same then the given triangles are similar.

Let's Understand the above theorem :-

The dimensions of rectangle 1 are x and y

Now,

• Rectangle 2 is made by multiplying each dimensions of rectangle 1 by a factor of k .

Let assume the value of K be 5

Therefore,

The dimensions of rectangle 2 are

$\sf{ 5x \:and \:5y }$

Now, The ratios of dimensions of both the rectangle :-

• $\bold{Rectangle 1 = Rectangle 2}$

$\bold{\dfrac{ x }{y}}{\bold{ = }}{\bold{\dfrac{5x}{5y}}}$

$\bold{\blue{\dfrac{ x }{y}}}{\bold{\blue{ = }}}{\bold{\blue{\dfrac{x}{y}}}}$

From above,

We can conclude that the ratios of both the rectangles are same

Hence , Both the rectangles are similar

Answer 2 :-

Here,

We have to proof that, the

• Perimeter of rectangle 2 = k(perimeter of rectangle 1 )

In the previous questions, we have assume the value of k = 5

Therefore,

According to the question,

Perimeter of rectangle 1

$\sf{ = 2( length + Breath) }$

$\bold{\pink{= 2( x + y ) }}$

Thus, The perimeter of rectangle 1

Perimeter of rectangle 2

$\sf{ = 2( length + Breath) }$

$\sf{ = 2(5x + 5y) }$

$\sf{ = 2 × 5( x + y) }$

$\bold{\pink{= 10(x + y) }}$

Thus, The perimeter of rectangle 2

According to the given condition :-

• Perimeter of rectangle 2 = k( perimeter of rectangle 1 )

Subsitute the required values,

$\sf{ 2(x + y) = 10(x + y)}$

$\bold{\pink{2x + 2y = 5(2x + 2y) }}$

From Above,

We can conclude that the, Perimeter of rectangle 2 is 5 times of perimeter of rectangle 1 and we assume the value of k = 5.

Hence, The perimeter of rectangle 2 is k times of rectangle 1

Answer 3 :

Here,

We have to proof that ,

• The area of rectangle 2 is k² times of the area of rectangle 1.

That is,

• Area of rectangle 1 = k²( Area of rectangle)

Therefore,

According to the question,

Area of rectangle 1

$\sf{ = Length × Breath }$

$\sf{ = x × y }$

$\bold{\red{= xy }}$

Area of rectangle 2

$\sf{ = Length × Breath }$

$\sf{ = 5x × 5y }$

$\bold{\red{ = 25xy }}$

According to the given condition :-

• Area of rectangle 1 = k²( Area of rectangle)

$\sf{ xy = 25xy }$

$\bold{\red{xy = (5)²xy }}$

From Above,

We can conclude that the, Area of rectangle 2 is (5)² times of area of rectangle 1 and we have assumed the value of k = 5

Hence, The Area of rectangle 2 is k times of rectangle 1 .