Question

Perimeter 40 cm area 100 square find length and breath?

Answer 1

Answer:

The length  = 10 cm and the breadth = 10 cm.

Step-by-step explanation:

Given perimeter = 40 cm

We know that, perimeter = 2( L + B)

Therefore, 2( L + B) = 40

                  L + B = 40/2 = 20

                  L = 20 - B .................(1)

Now. given area = 100 square cm

We know that, Area of rectangle = L × B

Therefore, L × B = 100   .....................(2)

Now substituting value of equation (1) in equation (2) we get,

(20 - B) B = 100

20 B - B² = 100

B² -20 B +100 =0

B² -10 B - 10 B +100 = 0

B(B - 10) - 10(B - 10) =0

B- 10 = 0

B = 10 cm ...................(3)

Substituting value of (3) in equation (1) we get,

L= 20 - 10

L = 10 cm

Answer 2

let length = l
and breadth = b
so perimeter = 2(l + b)
• 2(l + b) = 40
• (l + b) = 20
•l = 20 - b ..........(1)
also area = length × breadth
• l × b = 100
• (20 - b) × b = 100 (putting value of l from (1))
•
$20b - {b}^{2} = 100 \\ 20b - {b}^{2} - 100 = 0 \\ - ( {b}^{2} - 20b + 100) = 0 \\ {b}^{2} - 20b + 100 \\ ( {b)}^{2} - 2(b)10 + {(10)}^{2} = 0 \\ {(b - 10)}^{2} = 0 \\ (b - 10) = 0 \\ b = 10$
so breadth = 10
and length = b - 10 = 20 - 10 = 10
hope it helps u