The area of a square is twice that of a rectangle. The perimeter of the rectangle is 10cm. If it's length and breath each is increased by 1 cm, the area of the rectangle becomes equal to the area of the square. The length of side of the square is?
Answers
Step-by-step explanation:
Area of square = a²
Arean of rectangle = l×b
In first part of question
Area of square = 2 × area of rectangle
a² = 2 × l × b ......(1)
Perimeter of rectangle = 2( l+b)
10 = 2( l+b)
5 = l+b
5 - b = l........( 2 )
Putting equation in 2 in 1
a² = 2 × l × b
a²= 2b( 5-b)
a²= 10b - 2b².....(3)
In second part of question
Area of new rectangle = l + 1 × b + 1
= 5 - b + 1 × b + 1
= 6 - b × b + 1
= 6b - 6 - b² - b
= -b² + 5b - 6...... (4)
Area of new triangle = area of square
-b² + 5b - 6 = a²
-b²+ 5b - 6 = 10b -2b² ( from equation 2)
Now solve the equation and you will get breath and then put this breath on equation 2