Question

Find the length of the plot, where the length is one more than twice its breadth and the area is 136 m2Find the length of the plot, where the length is one more than twice its breadth and the area is 136 m2Find the length of the plot, where the length is one more than twice its breadth and the area is 136 m2Find the length of the plot, where the length is one more than twice its breadth and the area is 136 m2

Answer 1

Here we have to find the length of the plot, whose length is one more than twice it's breadth, and the area of the plot is 136 m² .

Let us start by defining the breadth of the plot as a variable, x

The length of the plot is one more than twice it's breadth

So, the length of the plot can be expressed in terms of its breadth as (2x+1)

The area of the plot can be written as Length × Breadth

That is x(2x+1)

But, the area of the plot is given to be 136 m²

Hence

x(2x+1) = 136

>> 2x² + x = 136

>> 2x² + x - 136 = 0

>> 2x² + 18x - 17x - 136 = 0

>> 2x( x + 9) - 17( x + 9) = 0

>> (2x - 17)(x + 9) = 0

x is either -9 or 17/2 = 8.5

Now, x is a length, which can't have a negative value

So, x has to be 8.5

The breadth of the plot is 8.5 cm

Thus, the length of the plot is (8.5 × 2) + 1 = 18 cm

Answer : The length of the plot is 18 cmHere we have to find the length of the plot, whose length is one more than twice it's breadth, and the area of the plot is 136 m² .

Let us start by defining the breadth of the plot as a variable, x

The length of the plot is one more than twice it's breadth

So, the length of the plot can be expressed in terms of its breadth as (2x+1)

The area of the plot can be written as Length × Breadth

That is x(2x+1)

But, the area of the plot is given to be 136 m²

Hence

x(2x+1) = 136

>> 2x² + x = 136

>> 2x² + x - 136 = 0

>> 2x² + 18x - 17x - 136 = 0

>> 2x( x + 9) - 17( x + 9) = 0

>> (2x - 17)(x + 9) = 0

x is either -9 or 17/2 = 8.5

Now, x is a length, which can't have a negative value

So, x has to be 8.5

The breadth of the plot is 8.5 cm

Thus, the length of the plot is (8.5 × 2) + 1 = 18 cm

Answer : The length of the plot is 18 cm

Answer 2

The question is that, we have to find the length of the plot where it is one more than twice it's breadth and the area is 136 m².

Let the breadth be x and the length be 2x + 1.

$\sf\purple{\underline{Area\:of\:the\:plot\:=\:Length\:×\:Breadth}}$

So, Area of the plot = x(2x + 1)

➸ Given Area = 136 m²

➸ 136 = x(2x + 1)

➸ 136 = 2x² + x

➸ x + 2x² - 136 = 0

By using the splitting the mid-term factor, we get

➸ 2x² + 18x - 17x - 136 = 0

➸ 2x (x + 9) - 17 (x + 9) = 0

➸ (x + 9)(2x - 17) = 0

➸ So, We get x as 17/2 = 8.5

Now, we found x = 8.5 m as breadth.

The length = 2x + 1

= 2(8.5) + 1

= 17 + 1

= 18 m

Therefore,$\sf\orange{Length = 18 m}$