Chapter ISG, Problem 3.8.14P

To determine

To calculate length and perimeter of S’s rectangle

Answer to Problem 3.8.14P

The sides are 24.88 and 3.55

Perimeter is 64 inches

Explanation of Solution

Given information:

B’s rectangle is 12 inches by 30 inches

S’s rectangle has one length 8inches longer than other.

Perimeter of S’s rectangle is 20 inches less than perimeter of B’s rectangle.

Formula used: Perimeter of rectangle is,

  $perimeter=2(l+w)$

Calculation:

For perimeter of B’s rectangle, substituting the values,

  $perimeter=2\times (12+30)$

So,

  $perimeter=2\times 42$

On solving,

  $perimeter=84$

Perimeter of B’s rectangle is 84 inches.

Hence, S’s rectangle’s perimeter is,

  $=84-20$

On solving,

  $=64$

Hence, perimeter of S’s rectangle is 64inches.

Let, one side of S’s rectangle be “x”

Hence, the other side will be “8x”

Substituting the values in perimeter formula,

  $64=2(x+8x)$

So,

  $64=2(9x)$

So,

  $64=18x$

Cross- multiplying both sides,

  $x=\frac{64}{18}$

On solving,

  $x=3.55$

Therefore, one of the side is 3.55

Hence, the other side is,

  $=8\times 3.55$

On solving,

  $=28.44$

Hence, the other side is 28.44