Question

The area of a rectangular plot is 374 m? The length of the plot (in metres) is one more than thrice its breadth. We need to find the length and breadth of the plot.


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Answer 1

Answer:

length = 34, breadth = 11

Step-by-step explanation:

For a rectangular plot we have that the area is the length times the breadth or as an equation:

$A = lb$.

We also know from the question that the length is one more than thrice the breadth:

$l = 3b+1$.

Then

$A = (3b+1)b = 3b^2+b$.

We know from the question that A = 374, hence

$3b^2+b=374$.

We can rearrange this to get a quadratic expression equal to zero

$3b^2+b-374=0$.

Using the abc-formula (or your favorite way of solving quadratic equations) we get:

b = 11, or b= $-\frac{34}{3}$.

As we cannot have negative breadth, as it is a distance, then b=11.

As $l = 3b+1$, then $l = 33+1 = 34$.

Thus we have our answer: $l = 34, b = 11$.

Answer 2

GIVEN ⤵️

Let the breadth of a rectangle = x m.

Thrice its breadth=3x m

Length of a rectangle= 3x-6 m

Perimeter of a rectangle = 2(l+b)

=2(3x−6+x)

=2(4x−6)

=8x−12

But we are given perimeter=148 m

8x−12=148

8x=148+12

8x=160

x=20 metres

Breadth=x= 20 metres

and Length=3x−6=3×20−6=60−6=54 metres.