A piece of card, 7 cm by 11 cm, has a square hole cut out of it. A second piece of card 8cm by 13cm, has four square holes, the same size as the first, cut out

Question

A piece of card, 7 cm by 11 cm, has a square hole cut out of it. A second piece of card 8cm by 13cm, has four square holes, the same size as the first, cut out of it. The area of card left is the same in each case. What is the side length of the hole?

Answer 1

Lucy,

 

Let x cm be the length and width of square hole cut.

 

Area of square hole cut is x*x = x^2 sq cm

 

Area of card left for first card is: Area of card - area of square hole

 

= 7*11 - x^2 = 77 -x^2

 

Similarly area of card left for second card = 8*13 - 4*x^2 (Since 4 squares are cut)

 

= 104 -4x^2

 

The areas are equal so 77 -x^2 = 104 -4x^2

Solving 3x^2 = 27 or x = 3

 

The length of hole is 3 cm.