Question

A machine part is made by cutting a small square from the centre of a large square piece of

steel.
The dimensions of the machine part are shown on the diagram.
All measurements are in cm.
3x + 4
+ 4
3
+ 4
The perimeter of the small square is two thirds of the perimeter of the large square.
Work out the length of a side of the small square.​

Answer 1

5 1/3 cm

Explanation:

If the perimeter of the small square is 2/3 of the perimeter of the large square, then the sides have that same ratio:

(x +4) = 2/3(3x +4)

x +4 = 2x +8/3

4/3 = x . . . . . . . subtract (x+8/3)

Then the side length of the small square is ...

4/3 +4 = 5 1/3 . . . cm