Question

7. A 5 x 5 square and a 3 x 3 square can be cut into pieces that will fit together to form a
third square

(a) Find the length of a side of the third square.

{b) In the diagram shown here, mark P on segment DC so that PD = 3, then draw
segments PA and PF. Calculate lengths of these segments.

(c) PA and Pf divided the squares into pieces. Arrange the piece to form the third square.

8. (Continuation) Change the sizes of the squares to AD = 8 and EF = 4. And redraw the
diagram. Where should the point P be marked this time> Form the third square again.

9. (Continuation) Will the preceding method always produce pieces that form a new
square? If your answer is yes, prepare a written explanation. If your answer is no, prepare
a counterexample - two specific squares that cannot be converted to a single square.​

Answer 1

Given :   A 5 x 5 square and a 3 x 3 square can be cut into pieces that will fit together to form a  third square

To find : the length of a side of the third square.

Solution:

Area of 5 * 5 square 25 sq units

area of  3 * 3 Square  = 9 sq units

Total area =  25 + 9 = 34 sq units

Side of new square  =√34  units

the length of a side of the third square.  = √34  units

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