Problem Setup:
- Let the length of the rectangular field be $L$ and the breadth be $B$.
- The ratio of length to breadth is given as $L : B = 6 : 5$.
- We can represent the length as $L = 6x$ and the breadth as $B = 5x$ for some common multiplier $x$.
- It is stated that the breadth is 25 m less than the length, which means $B = L - 25$ or $L - B = 25$.
Finding the Dimensions
Substitute the expressions for $L$ and $B$ in terms of $x$ into the difference equation:
$L - B = 25$
Substituting $L = 6x$ and $B = 5x$:
$6x - 5x = 25$
Solving for $x$:
$x = 25$
Now, calculate the actual length and breadth:
- Length $L = 6x = 6 \times 25 = 150$ m
- Breadth $B = 5x = 5 \times 25 = 125$ m
Check: The difference $L - B = 150 - 125 = 25$ m, which matches the given information.
Calculating the Perimeter
The formula for the perimeter $P$ of a rectangle is:
$P = 2(L + B)$
Substitute the calculated values of $L$ and $B$:
$P = 2(150 \text{ m} + 125 \text{ m})$
$P = 2(275 \text{ m})$
$P = 550 \text{ m}$
Therefore, the perimeter of the field is 550 m.
Similar Questions
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- A sector of a circle has a radius of $18\text{ cm}$ and a central angle of $125^\circ$. What will be its approximate perimeter?
(Use $\pi = \frac{22}{7}$) - Area of a square is equal to ten times the area of a rectangle of edge 5 cm $\times$ 8 cm. What is the perimeter of the square?
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Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
