Question

Write an inequality to match each description. Use n for the variable.

A rectangle has a perimeter of 26 units and an area of more than 30 square units.

Answer 1

`{\huge {\mathfrak {Answer :-}}}`

Let, the length be l and breadth be b.

So, 2(l + b) = 26

Or, l + b = 13

Or, l = 13 - b

So, we may write like this,

Area = l * b

Or, l * b > 30

Or, l (13 - l) > 30

Or, 13l - l^2 > 30

Or, l^2 - 13l + 30 > 0

Or, l^2 - 3l - 10l + 30 > 0

Or, l(l - 3) - 10(l - 3) > 0

Or, (l - 3)(l - 7) > 0

Or, l - 7 > 0

Or, l > 7.

Now, putting the value of l,

We get, l * b > 30

Or, 7 * b > 30

Or, b > 30/7

➡️ Therefore, we get,

Length > 7

Breadth > 30/7

`<b>` That's it..