Question

find the length and width of the rectangle whose perimeter is 40 cm and area is 100 square cm​

Answer 1

Step-by-step explanation:

Area of rectangle = length × breadth = l × b

Perimeter of rectangle = 2(l+b)

Given, A = 100 squarecm

And P = 40cm

Hence

2(l+b) = 40

• l + b = 40/2
• l + b = 20
• l = 20 - b ----- 1

l × b = 100

• Substituting 1 in this equation
• (20 - b)b = 100
• 20b - b^2 =100
• b^2 - 20b + 100 = 0
• b^2 - 10b - 10b + 100 = 0 (splitting the middle term)
• b(b -10) - 10 (b-10)
• (b-10) (b-10) = 0

Hence b = 10 cm

From 1, l = 20 - b

Hence l = 10 cm