Question

a rectangular sign has a length of 3 and 1/2 ft and width of 1 and 1/8 ft will the area of the sign be greater or less than 3 and 1/2 ft, how do you know? What is the area of the sign?

Answer 1

Answer:

The area is 3.9375 cubic ft, so yes, the area will greater than 3 and 1/2 ft.

Hope this helps:)

Step-by-step explanation:

Answer 2

Length of a rectangular sign :-

$= 3 \frac{1}{2} \: \: m$

Width of a rectangular sign :-

$= 1 \frac{1}{8} \: \: m$

We know that :-

The formula for finding the area of a rectangle is :-

$=\bold{ length \times breadth}$

Which means :-

The area of the rectangular sign:-

$=3 \frac{1}{2} \times 1 \frac{1}{8}$

$= \frac{(2 \times 3 )+ 1}{2} \times \frac{(8 \times 1) + 1}{8}$

$= \frac{6 + 1}{2} \times \frac{8 + 1}{8}$

$= \frac{7}{2} \times \frac{9}{8}$

$= \frac{7 \times 9}{2 \times 8}$

$= \frac{63}{16}$

$={3 \frac{15}{6} \: \: }$

$= 3 \frac{15 \div 3}{6 \div 3}$

$={ 3 \frac{5}{2} \: m}$

Thus, the area of the rectangular sign is:-

$=\bold{ 3 \frac{5}{2} \: m}$

We can see that :-

$\bold{3 \frac{5}{2} \: > 3 \: \frac{1}{2} \: }$

Which will mean that the area of the rectangular sign is greater than ${ 3 \frac{1}{2} \: m}$.

Therefore, the area of the rectangular sign is = $\bold{ 3 \frac{5}{2} \: m}$ and it is greater than $\bold{ 3 \frac{1}{2} \: m}$ .