Question

The perimeter of a rectangular swimming pool is 164 m. Its length is 3 m more than twice its breadth. What are the length and the breadth of the pool ?

Answer 1

Step-by-step explanation:

Answer

length =55.66

breadth =26.33

Step-by-step explanation:

GIVEN THAT

PERIMETER =164

let breadth =x

let length =2x+3

2 (l+b)=PERIMETER

2(2x+3+x) = 164

2 (3x+3) = 164

6x+6 =164

6x =164-6

6x =158

x =158/6

x =26.33

length =2x+3=55.66

breadth=x=26.33

CHECKING THE SUM

perimeter =2 (l+b)

2 (55.66 + 26.33)

2 (81.99)

163.98

163.98 is approximately equal to 164

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Answer 2

Given:

Perimeter of swimming pool = 164 m

Length = 2*breadth + 3 m

Answer:

Explanation:

Let the breadth of the swimming pool be x.

Length = 2*x + 3m

Length = (2x+3) m

ATQ,

Perimeter = 2( Length + Breadth )

164 m = 2( 2x+3 + x ) m

Dividing both sides by 2, we get:

82 m = 3x + 3 m

Subtracting both sides by 3 , we get:

3x + 3 - 3 = 82 - 3 m

3x = 79

Dividing both sides by 3, we get:

$x = \frac{79}{3}$

$\tt \: breadth \: = \: \frac{79}{3} \: m$

$\therefore \: \tt \: length = (2 \times breadth \: + 3) \: m$

$\implies \: (2 \times \frac{79}{3} + 3) \: m$

$\implies \: (\frac{158}{3} + 3) \: m$

Taking LCM, we get :

LCM = 3

$\implies \: \frac{158 + 9}{3} \: m$

$\implies \: length \: = \: \frac{167}{3} \: m$

Proof :

Perimeter = 2( Length + Breadth )

$164 \: m \: = 2( \frac{167}{3} + \frac{79}{3} ) \: m$

Taking LCM, we get :

LCM is 3

$164 \: m = 2( \frac{246}{3} ) \: m$

Dividing both sides by 2, we get :

$82 \: m \: = \: \frac{246}{3} \: m$

Dividing RHS by 3, we get:

$82 \: m \: = \: 82 \: m$

LHS = RHS

Hence Proved .

Formulas :

1) Area of rectangle = Length * Breadth

2) Perimeter of rectangle = 2( Length + Breadth )

3) Cost of fencing a rectangular plot when cost of fencing is given in per units( e.g.cost is in m) = Perimeter of plot * Cost of fencing per unit.

4) Cost of fencing a rectangular plot when cost of fencing is given in per units²( e.g.cost is in m²) = Area of plot * Cost of fencing per unit².