Question

3 the rectangle below is divided into square regions. using the information given, find the area of each of these regions. is the outside rectangle a square also? 4 show that two wrongs can make a right. replace each different letter in the addition below with a different digit. it is required that o = zero. wrong + wrong right

Explanation:

Step1: Find side - lengths of known squares

Since the area of a square is $A = s^{2}$, for the square with area 81 square units, $s_{1}=\sqrt{81}=9$ units. For the square with area 64 square units, $s_{2}=\sqrt{64}=8$ units.

Step2: Find side - length of square A

The side - length of square A is the difference between the side - lengths of the 81 - square - unit and 64 - square - unit squares. So, $s_A=9 - 8=1$ unit, and the area of square A is $A_A = 1\times1 = 1$ square unit.

Step3: Find side - length of square D

The side - length of square D is equal to the side - length of the 64 - square - unit square, so the area of square D is 64 square units.

Step4: Find side - length of square E

The side - length of square E is equal to the side - length of square A, so the area of square E is 1 square unit.

Step5: Find side - length of square B

The side - length of square B is the sum of the side - lengths of square A and square E, so $s_B=1 + 1=2$ units, and the area of square B is $A_B=2\times2 = 4$ square units.

Step6: Find side - length of square C

The side - length of square C is the sum of the side - lengths of square B and square E, so $s_C=2 + 1=3$ units, and the area of square C is $A_C=3\times3 = 9$ square units.

Step7: Find side - length of square F

The side - length of square F is the sum of the side - lengths of the 64 - square - unit square and square D, so $s_F=8+8 = 16$ units, and the area of square F is $A_F=16\times16 = 256$ square units.

Step8: Find side - length of square G

The side - length of square G is the sum of the side - lengths of square C and square E, so $s_G=3 + 1=4$ units, and the area of square G is $A_G=4\times4 = 16$ square units.

Step9: Check if the outer rectangle is a square

The horizontal side - length of the outer rectangle is $9+2 + 3=14$ units. The vertical side - length of the outer rectangle is $8 + 8+1+1=18$ units. Since the horizontal and vertical side - lengths are not equal, the outer rectangle is not a square.

Answer:

Area of A: 1 square unit
Area of B: 4 square units
Area of C: 9 square units
Area of D: 64 square units
Area of E: 1 square unit
Area of F: 256 square units
Area of G: 16 square units
The outer rectangle is not a square.