The diffrence of the area of of two squares drawn on two lines segments of different length is 32 sq.cm. Find the length of the greater line segment if one is longer than the other by 2 cm.
The diffrence 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.
[A]16 cm
[B]11 cm
[C]9 cm
[D]7 cm
9 cm
Let the length of the smaller line segment = x cm.
The length of largest line segment = (x+2) cm.
According to the question $latex \left ( x+2 \right )^{2}-x^{2}=32$
$latex =>x^{2}+4x+4-x^{2}=32$
$latex =>4x=32-4=28$
$latex =>x=\frac{28}{4}=7&s=1$
Therefore The required lenght = x+2 = 7+2 = 9 cm.
Hence option [D] is the right answer.