Question

the distance around a rectangular field is 400 metres in the field is 26 more than the breadth calculate the length and breadth ​

Answer 1

${\underline {\underline {\Large {\bf \gray { Correct \: Question } }}}}$

The distance around a rectangular field is 400 metres. The length of the field is 26 meters more than the breadth. Calculate the length and breadth of the field.

${\underline {\underline {\Large {\bf \gray { How \: to \: solve? } }}}}$

• Here we are given that, the distance around a rectangular field is 400 metres which is actually its perimeter.

• Also,given that length of the field is 26 meters more than the breadth.

• We'll assume the breadth as "x" then the length will become "26 + x".

• Then we'll put the value in the formula of perimeter of rectangle to find our the value of x.

• The value of "x" will be its breadth, and length 26 more than the value of x.

${\underline {\underline {\Large {\bf \gray { Required \: solution: } }}}}$

Given:

• Perimeter of rectangle = 400m
• Length = 26 more than breadth.

To find:

• Breadth and length of the rectangle

Calculation:

Let's assume the breadth as x m.

• Therefore,its length becomes "26 + x"

We know that,

${\underline {\boxed {\large {\bf \gray { Perimeter \: of \: rectangle = 2 ( l +b) } }}}}$

$\longmapsto$ 400 = 2 ( x + 26 + x )

$\longmapsto$ 400 = 2 ( 2x + 26 )

$\longmapsto$ $\sf { \dfrac{400}{2} }$ = 2x + 26

$\longmapsto$ 200 = 2x + 26

$\longmapsto$ 2x = 200 - 26

$\longmapsto$ 2x = 174

$\longmapsto$ x = $\sf { \dfrac{174}{2} }$

$\longmapsto$ x = 87 m.

Therefore,

• Length = x = 87m
• Breadth = 26 + x

= 26 + 87

= 113m

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Extra!!

Perimeter:

• Perimeter of square : 4 × side
• Perimeter of rectangle : 2 ( l + b )
• Perimeter of parallelogram : 2 ( l + b )
• Perimeter of rhombus : 4 × side
• Perimeter of trapezium : Sum of sides
• Perimeter of triangle : Sum of sides
• Perimeter of circle (circumference) : 2πr

Area:

• Area of square : (Side)²
• Area of rectangle : l × b
• Area of parallelogram : Base × height
• Area of rhombus : ½ × diagonal$\sf {_1}$ × diagonal$\sf {_2}$
• Area of trapezium : ½ × (sum of parallel sides) × h
• Area of triangle : ½bh
• Area of circle : πr²

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