Question

the perimeter of a square exceeds that of another by 24 cm and the area of the larger square is 84 sq cm more than the area of the smaller one. Find the length of the two sides.

Answer 1

Answer:

Solution



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Let S1 and S2 be two squares. Let the side of the square S2 be x cm in length. 

Then, the side of square S1 is (x+4)cm

Area of square S1=(x+4)2

and Area of square S2=x2

It is given that,

(Area of square S1)+(Area of square S2)=400cm2

⇒(x+4)2+x2=400

⇒(x2+8x+16)+x=400⇒2x2+8x−384=0⇒x2+4x−192=0

⇒x2+16x−12x−192=0⇒(x+16)(x−12)=0⇒x=12orx=−16

As the length of the side of a square cannot be negative. Therefore, x=12

Side of square S1=x+4=12+