Question

Two square have side xcm and (x+4)cm the sum of their areas is 656cm². find the sides of the square

Answer 1

sorry for my wrong calculation

Answer 2

∵ Sides are xcm and (x+4)cm

∴ The areas of the squares will be x² cm² and (x+4)² cm² respectively

∴ According to the condition,

x² cm² + (x+4)² cm² = 656cm²

or,( x² + x² + 4² + 2×4×x) cm² = 656cm²

or, 2x² + 8x + 16 - 656 = 0

or, 2x² + 8x - 640 = 0

or, 2(x² + 4x - 320) = 0

or, x² + 20x - 16x - 320 = 0

or, x(x+20) - 16(x+20) = 0

or, (x+20)(x-16) = 0

∴ x = 16,-20

∵ length can't be -ve

∴ x= 16 cm

& x+4 = 16cm + 4 = 20cm

∴ sides of the squares are 16cm & 20cm respectively.