Chapter ISG, Problem 8.4.3P

a.

To determine

To compare area of squares

Answer to Problem 8.4.3P

2s+1 is change in area.

Explanation of Solution

Given:

Side of sqaure₁= $s$

Side of sqaure₂= $s+1$

Calculation:

Area of square=(side)2

Area of square₁= $s^2$

Area of square₂= ${(s+1)}^2$

Solving using identity ${(a+b)}^2=a^2+b^2+2ab$ ,

  ${(s+1)}^2=s^2+1^2+2(s)(1)$

So,

  ${(s+1)}^2$ = $s^2+1+2s$

Change in area=area of square₂- Area of square₁

  = $s^2+1+2s$ - $s^2$

  =2s+1 Hence, 2s+1 is change in area.

b.

To determine

To compare area of squares

Answer to Problem 8.4.3P

2s +3 is change in area.

Explanation of Solution

Given:

Side of sqaure₁= $s$

Side of sqaure₂= $s+1$

Calculation:

Area of square=(side)2

Area of square₁= ${(s+1)}^2$

Solving using identity ${(a+b)}^2=a^2+b^2+2ab$ ,

  ${(s+1)}^2=s^2+1^2+2(s)(1)$

So,

  ${(s+1)}^2$ = $s^2+1+2s$

Area of square₂= ${(s+2)}^2$

Solving using identity ${(a+b)}^2=a^2+b^2+2ab$ ,

  ${(s+1)}^2=s^2+2^2+2(s)(2)$

So,

  ${(s+2)}^2$ = $s^2+4+4s$

change in area=area of square₂- Area of square₁

  = $s^2+4+4s$ -( $s^2+1+2s$ )

  = 2s +3 Hence, 2s +3 is change in area.

c.

To determine

To compare area of squares

Answer to Problem 8.4.3P

2s +5 is change in area.

Explanation of Solution

Given:

Side of sqaure₁= $s$

Side of sqaure₂= $s+1$

Calculation:

Area of square₂= ${(s+2)}^2$

Solving using identity ${(a+b)}^2=a^2+b^2+2ab$ ,

  ${(s+2)}^2=s^2+2^2+2(s)(2)$

So,

  ${(s+2)}^2$ = $s^2+4+4s$

Area of square₂= ${(s+3)}^2$

Solving using identity ${(a+b)}^2=a^2+b^2+2ab$ ,

  ${(s+3)}^2=s^2+3^2+2(s)(3)$

So,

  ${(s+3)}^2$ = $s^2+9+6s$

Change in area=area of square₂- Area of square₁

  = $s^2+3^2+2(s)(3)$ -( $s^2+4+4s$ )

Solving,

  = 2s +5 Hence, 2s +5 is change in area.

d.

To determine

To find how much the area.

Answer to Problem 8.4.3P

The area will be will 2a +1

Explanation of Solution

Given:

Side₁= a

Side₂= a +1

Calculation:

Based on parts above, the change in the area will be ${(a+1)}^2-a^2$ . Hence, solving the terms,

The change of area= 2a +1.