Question:If the diagonal of a rectangle and a square, each is equal to 80 cm and the difference of their areas is 100 sq. cm, the side of the rectangle are :
A `35 cm, 15 cm`
B `30 cm, 10 cm`
C `28 cm, 12 cm`
D ` 25 cm, 15 cm`
+ Explanationperimeter of square = 80 cm. So, side of square = 20 cm.
Area of the square` = (20 xx 20) cm^2`
`= 400 cm^2`
With same perimeters, area of the square is larger.
:. Area of rectangle`= (400 - 100) cm^2`
`= 300 cm^2`
Let length of rect. = x & its breadth = y. Then,
xy = 300 and x + y = 40
`:. (x - y) = sqrt((x + y))^2- 4xy`
`= sqrt(1600 - 1200) = 20`
Solving `x + y = 40 & x - y = 20,` we get` x = 30, y = 10`
:. Sides are` 30 cm, 10 cm.`
