Name: Operations on Mixed Fractions
Uploaded: 2019-07-19
Duration: 19 min 35 s
Description: We can perform arithmetic operations on mixed fractions, too. In this video, we learn some operations on mixed fractions along with converting a mixed fraction into an improper fraction.

Question

The perimeter of the given figure is $18 m$ and the area of rectangular part $A C E F$ is $8 \frac{1}{2} m^{2}$ . Find the length and breadth of the rectangular part.

Accepted Answer

Given figure:

The perimeter is the length around boundary of a close figure.

So, perimeter of the figure is: $A B + B C + C D + D E + E F + F G + G A$ .

Let, $E F = x m$

So,

$2 \frac{1}{2} + 3 \frac{2}{3} + 1 \frac{1}{4} + 1 \frac{2}{3} + x + 1 \frac{3}{4} + 1 \frac{1}{2} = 18 \Rightarrow (2 + 3 + 1 + 1 + x + 1 + 1) + (\frac{1}{2} + \frac{2}{3} + \frac{1}{4} + \frac{2}{3} + \frac{3}{4} + \frac{1}{2}) = 18 \Rightarrow (9 + x) + (\frac{6 + 8 + 3 + 8 + 9 + 6}{12}) = 18 \Rightarrow 9 + x + \frac{40}{12} = 18 \Rightarrow x + \frac{10}{3} = 9 \Rightarrow x = 9 - \frac{10}{3} \Rightarrow x = \frac{27 - 10}{3} \Rightarrow x = \frac{17}{3}$

Length of $E F = \frac{17}{3} m$

Area of rectangle $= length \times breadth$

$∴ A F \times E F = 8 \frac{1}{2} \Rightarrow A F \times \frac{17}{3} = \frac{17}{2} \Rightarrow A F = \frac{3}{2}$

So, length and breadth of the rectangular part is $\frac{17}{3} m$ and $\frac{3}{2} m$ .

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