Chapter ISG, Problem 2.4.5P

a.

To determine

To label the side lengths

Answer to Problem 2.4.5P

For garden A, length is $2x+2$ and breadth is x units

For garden B, length is $2.5(x-1)$ and width is $x-1$ units

Explanation of Solution

Given information:

Length and breadth of gardens

Calculation:

Garden A

Let the breadth be x, according to question,

Length= $2x+2$

Hence length is $2x+2$ and breadth is x.

Garden B

Width= $x-1$

Length = $2.5(x-1)$

Hence, length is $2.5(x-1)$ and width is $x-1$ .

b.

To determine

To write an expression

Answer to Problem 2.4.5P

For garden A, perimeter is $6x+4$

For garden B, perimeter is $7x-3$

To solve the equation, distributive property is used.

Explanation of Solution

Given information:

Length and breadth of garden

Formula used:

Perimeter of triangle= 2(length+ breadth)

Calculation:

For garden A,

Length= $2x+2$

Breadth= x

Substituting values,

Perimeter= $2(2x+2+x)$

Solving,

Perimeter= $2(3x+2)$

On solving,

Perimeter= $6x+4$

Hence, perimeter is $6x+4$ .

For garden B,

Length= $2.5(x-1)$

Breadth= $x-1$

Substituting values,

Perimeter= $2\{2.5(x-1)+x-1\}$

Solving,

Perimeter= $2\{2.5x-2.5+x-1\}$

So,

Perimeter= $2\{3.5x-1.5\}$

Hence, perimeter is $7x-3$ .

To solve the equation, distributive property is used.

c.

To determine

To write an equation

Answer to Problem 2.4.5P

Difference between both perimeters is x-7

Explanation of Solution

Given information:

Perimeters of garden

Calculation:

Perimeter of garden A is $6x+4$

Perimeter of garden B is $7x-3$

Now,

Subtracting both perimeters,

Perimeter B- perimeter A= $7x-3$ -( $6x+4$ )

Solving,

= $7x-6x-3-4$

So,

= $x-7$

Hence, garden B is $x-7$ bigger than garden A.

d.

To determine

To write the dimension of gardens

Answer to Problem 2.4.5P

For garden A, length is 16 and breadth is 7

For garden B, length is 15 and breadth is 6

Explanation of Solution

Given information:

Garden A and garden B

Calculation:

According to question,

Perimeter of both is same

So,

  $6x+4$ = $7x-3$

Solving,

  $7x-6x=4+3$

Hence, $x=7$

Dimensions of garden A is $2x+2$ and x

Solving,

Length= $2(7)+2$ , breadth=7

Hence, length is 16 and breadth is 7

And, dimension of garden B is $2.5x-2.5$ and $x-1$

Solving,

Length= $2.5(7)-2.5$ ,

On solving,

Length $=15$

For breadth,

Breadth= 7-1

On solving,

Breadth=6

Hence, length is 15 and breadth is 6

e.

To determine

To explain why solution is not reasonable

Answer to Problem 2.4.5P

The value of x is negative.

Explanation of Solution

Given information:

  $6x-4=5x-6$

Calculation:

Shifting right-hand side terms to left-hand side,

  $6x-5x=-6+4$

On solving,

  $x=-2$

It can be seen that value of x is negative which is not possible because x is a dimension