Let be the large piece and the small piece
The ratio of the card left is therefore given by
Since and that we can rewrite the above equation:
Note I have used the rule of surds which says that
Can you find using the same principles?
A large rectangular piece of card is square root of 5 + square root of 20 cm long and square root of 8 cm wide. A small rectangle square root of 2 cm long and square root of 5 cm wide is cut out of the piece of card. Express the area of the card that is left in a percentage of the area of the large rectangle?