Question

The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq. cm. find the length of the greater line segment if one is longer than the other by 2 cm.

Answer 1

let the first length of line segment = x
let the second length of line segment = x+2
area of first square=x×x
area of second square=( x+2)×(x+2)
according to the question
$(x + 2) {}^{2} - x {}^{2} = 32 \\ (x + 2 + x)(x + 2 - x) = 32\\ (2x + 2 ) \times 2 = 32 \\ 4x + 4 = 32 \\ 4x = 32 - 4 = 28 \\ x= 28 \div 4 = 7 \\ x = 7 cm \\ x = 7 + 2 = 9 \: cm$