Question

11. Write an expression for finding the perimeter and area of a rectangle in which the length is x m and the breadth of the rectangle is 3 metre less than the length. ​

Answer 1

Answer:

You’d start with the simple formula P=2(l+b)

Then, as we know l=4b−3 , we can plug that in to make

P=2(5b−3)

Now we know the value of the perimeter, P=94 , so we can plug that in

94=2(5b−3)

And we can simplify that to

47=5b−3

Simplify!

50=5b

Simplify!

10=b

So now we know that the breadth is 10m, we can plug that into l=4b−3 to get

l=4(10)−3

Simplify!

l=40−3

Simplify!

l=37

And there we go!

The length is 37m, and the breadth is 10m.

Step-by-step explanation:

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Answer 2

Given:

The length of the rectangle is $x$ metre.

The breadth of the rectangle is $3$ metre less than the length. ​

To Find:

The expression for finding the perimeter.

The expression for finding the area.

Solution:

From the given, we know

Length $=x$

Breadth $=x-3$

The formula for perimeter is twice the sum of length and breadth.

Now let us find the expression for the perimeter,

$=2(x+x-3)\\ \\ =2(2x-3)\\ \\= 4x-12$

The formula for the area is the product of length and breadth.

Now let us find the expression for the area,

$=x(x-3)\\\\=x^{2} -3x$

Hence, the expression for the perimeter is $4x-12$ and the expression for the area is $x^{2} -3x$.