Question

What will be the length of sides of a ractangle area, if it perimeter is 40 and area is 100 units.

Answer 1

This is your answer.....

Answer 2

Heya.
Here is the answer of your query.

Let the length of rectangle be and breadth be b.

It is given that the perimeter is 40units.
So. by using rectangle perimeter formula
P = 2(l +b)
40 = 2(l+b)
l+ b = 20
Hence. l = 20 - b ........(i)

Now, it is given that the area of rectangle is 100 units².

So, area of rectangle is lb
lb = 100. ...... (ii).

From equation (i) and (ii), we get
b (20 - b) = 100
20b - b² = 100
-b² + 20b - 100 = 0

Multiplying both sides by (-). we get
b² - 20b + 100 = 0

Now we have to find two numbers a and b such that a +b = -20 and ab = 100.

Clearly. we can see that these two numbers are -10 and -10.

So, b² -10b -10 b + 100 = 0
b ( b-10) -10 (b - 10) = 0.
(b - 10) (b- 10) =. 0

Comparing with 0.
We get b = 10.

Putting value of b in eq (i), we get l =10.

Hence, the length (L) = 10 units and bredth  (B) is 10 units.

Hope this helps