One side of a rectangular backyard is 2 meters longer than t

One side of a rectangular backyard is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?

let width of rectangular backyard = w

therefore, length of teh backyard would be w+2

as, One side of a rectangular backyard is 2 meters longer than the other

diagonal of rectangle = sqrt(w^2+l^2)

here l = (w+2)

diagonal given = 10 m

therefore we can write

10 = sqrt(w^2+l^2)

squareing both sides

100 = w^2 + (w+2)^2

100 = 2w^2 + 4 + 4w

2w^2 + 4w - 96 = 0

on solving the quadratic we get

w = 6

so width of the rectangular backyard = 6 metres

length of the rectangular backyard = (6+2) = 8 metres