Question

The dimension of a rectangular garden are 12 1/2 feet by 16 3/4 feet. If 1 5/8 feet is added to all the sides, find the new dimensions of the garden.

Answer 1

Answer: The new dimensions of the garden are $13\dfrac{1}{8}\ feet\ and\ 17\dfrac{3}{8}\ feet$

Step-by-step explanation:

Since we have given that

Old length of rectangular garden = $12\dfrac{1}{2}=\dfrac{25}{2}\ feet$

Old breadth of rectangular garden = $16\dfrac{3}{4}=\dfrac{67}{4}\ feet$

If $\dfrac{5}{8}$ feet is added to all the sides.

So, New length of rectangular garden is given by

$\dfrac{25}{2}+\dfrac{5}{8}\\\\=\dfrac{100+5}{8}\\\\=\dfrac{105}{8}\\\\=13\dfrac{1}{8}\ feet$

New breadth of rectangular garden is given by

$\dfrac{67}{4}+\dfrac{5}{8}\\\\=\dfrac{134+5}{8}\\\\=\dfrac{139}{8}\\\\=17\dfrac{3}{8}\ feet$

Hence, the new dimensions of the garden are $13\dfrac{1}{8}\ feet\ and\ 17\dfrac{3}{8}\ feet$

Answer 2

Answer:

$L=15\tfrac{6}{8} \ feet$

$B=20 \ feet$

Step-by-step explanation:

Given that the dimensions of a rectangular field is (in feet)

$l=12\tfrac{1}{2}=\frac{12 \times 2 +1}{2}=\frac{25}{2}$

$b=16\tfrac{3}{4}=\frac{16 \times 4 +3}{4}=\frac{67}{4}$

Now we are being told that $1\tfrac{5}{8}$ feet is added to each side. Hence New Dimensions will be

$1\tfrac{5}{8}=\frac{1 \times 8 +5}{8}=\frac{13}{8}$

$L = \frac{25}{2}+\frac{13}{8}+\frac{13}{8}$

$L=\frac{25 \times 4}{2 \times 4}+\frac{13}{8}+\frac{13}{8}$

$L=\frac{100}{8}+\frac{13}{8}+\frac{13}{8}$

$L= \frac{100+13+13}{8}$

$L= \frac{126}{8}$

$L=15\tfrac{6}{8}$

$B= \frac{67}{4}+\frac{13}{8}+\frac{13}{8}$

$B= \frac{67\times 2}{4\times 2}+\frac{13}{8}+\frac{13}{8}$

$B= \frac{134}{8}+\frac{13}{8}+\frac{13}{8}$

$B= \frac{134+13+13}{8}$

$B=\frac{160}{8}$

$B=20$

Hence New Dimensions are

$L=15\tfrac{6}{8} \ feet$

$B=20 \ feet$