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

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 1 2 + 3 2 3 + 1 1 4 + 1 2 3 + x + 1 3 4 + 1 1 2 = 18 ⇒ 2 + 3 + 1 + 1 + x + 1 + 1 + 1 2 + 2 3 + 1 4 + 2 3 + 3 4 + 1 2 = 18 ⇒ 9 + x + 6 + 8 + 3 + 8 + 9 + 6 12 = 18 ⇒ 9 + x + 40 12 = 18 ⇒ x + 10 3 = 9 ⇒ x = 9 - 10 3 ⇒ x = 27 - 10 3 ⇒ x = 17 3 Length of E F = 17 3 m Area of rectangle = length × breadth ∴ A F × E F = 8 1 2 ⇒ A F × 17 3 = 17 2 ⇒ A F = 3 2 So, length and breadth of the rectangular part is 17 3 m and 3 2 m .

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Find a number such that its two-thirds is equal to $\frac{5}{4}$ .

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Important Questions on Fractions

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Step by Step Mathematics>Chapter 2 - Fractions>HOTS QUESTIONS>Q 1

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.