Question

Which has more area , a square of side $11\frac{1}{2}$m , area of rectangle with sides $10\frac{1}{3}$ m and $12\frac{1}{2}$ m and by how much ?

Answer 1

Given : Sides of square is $11\frac{1}{2}\text{m}$ and sides of rectangle are $10\frac{1}{3}\text{and}12\frac{1}{2}$

Step 1 : Express the mixed fraction as simplest form

$11\frac{1}{2}=\frac{23}{2},10\frac{1}{3}=\frac{31}{3},12\frac{1}{2}=\frac{25}{2}$

Step 2 : Find the area of square

Area of the square $=side\times side$

$$\begin{gathered} =11\frac{1}{2}\times 11\frac{1}{2} \\ =\frac{23}{2}\times \frac{23}{2} \\ =\frac{529}{4}{\text{m}}^2 \end{gathered}$$

Step 3 : Find the area of rectangle
Area of rectangle $=length\times breadth$

$$\begin{gathered} =10\frac{1}{3}\times 12\frac{1}{2} \\ =\frac{31}{3}\times \frac{25}{2} \\ =\frac{775}{6}{\text{m}}^2 \end{gathered}$$

Step 4 : Find the greater area

LCM of $\left(4,6\right)=12$

$$\begin{gathered} \frac{529}{4}=\frac{529\times 3}{4\times 3}=\frac{1587}{12} \\ \frac{775}{6}=\frac{775\times 2}{6\times 2}=\frac{1550}{12} \\ 1587>1550 \\ \therefore \frac{1587}{12}>\frac{1550}{12} \\ \Rightarrow \frac{529}{4}>\frac{775}{6} \end{gathered}$$

Step 5 : Area greater by how much

$$\begin{gathered} \frac{1587}{12}-\frac{1550}{12} \\ \frac{1587-1550}{12} \\ \frac{37}{12} \end{gathered}$$

Hence, area of square is greater and it is greater by $\frac{37}{12}$