Can anyone please help me with this ?

Many thanks in advance

Can anyone please help me with this ?

Many thanks in advance

alfretztay

I have tweaked the above question as follows : The figure is made up of 2 big squares, 2 small squares and 1 rectangle. The perimeter of the rectangle ABCD is 24 cm. The total area of all 4 squares is 148 sq cm. (a) What is the area of the rectangle? (b) What is the length of (i) one big square and (ii) one small square?

(a)

24/2 = 12 (total length of 1 big square and 1 small square)

148/2 = 74 (total are of 1 big square and 1 small square)

12 x 12 = 144

144 – 74 = 70

70/2 = 35

(b)

(ii)

74 = 49 + 25 = 7 x 7 + 5 x 5

length of one big square = 7 cm

(ii)

length of 1 small square = 5 cm

Ans : (a) 35 sq cm; (b)(i) 7 cm and (ii) 5 cm.

Note :

The total area of all 4 squares could also be changed to 160 sq cm.

(a)

24/2 = 12 (total length of 1 big square and 1 small square)

160/2 = 80 (total are of 1 big square and 1 small square)

12 x 12 = 144

144 – 80 = 64

64/2 = 32

(b)

(ii)

80 = 64 + 16 = 8 x 8 + 4 x 4

length of one big square = 8 cm

(ii)

length of 1 small square = 4 cm

Ans : (a) 32 sq cm; (b)(i) 8 cm and (ii) 4 cm.

bbcxd

Perimeter of ABCD = 2AB + 2AD = 24 cm

=> 2 (AB + AD ) = 24

=> AB + AD^{ }= 12

Area of 4 squares = 2AB^{2} + 2AD^{2} = 150

=> 2 (AB^{2} + AD^{2} ) = 150

=> AB^{2} + AD^{2 }= 75

(AB + AD)^{2} = 12^{2 }=144

(AB + AD)^{2} = AB^{2} + AD^{2}^{ }+2 AB x AD

(AB + AD)^{2} = 75^{ }+2 AB x AD

Therefore,

75^{ }+2 AB x AD = 144

2 AB x AD = 144 – 75

2 AB x AD = 69

AB x AD = 34.5 cm

Area of ABCD = AB x AD = 34.5 cm