Question

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm square.
However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm square. Determine the sides of the two squares.

Answer for 50 points. Spams will be deleted.​

Answer 1

Answer:

Let the lengths of each side of the smaller square be x cm and that of the larger square be y cm.

Then, area of the smaller square=x 2 cm 2

y 2 −2x 2 =14....(i)

2y 2+3x 2 =203....(ii)

From (i) we have

y 2=14+2x 2

Substituting this value of y 2 in (ii) we get

⇒28+4x 2 +3x 2 =203⇒7x 2

=203−28

⇒7x 2=175⇒x 2

=25⇒x=5cm

Putting x=5 in (i) we get

y 2−2×5 2 =14⇒y 2

=64⇒y=8

Hence the lengths of the sides of the square are 5cm and 8cm respectively.