self Maths Puzzle

A square is cut from the centre of a rectangle. The length of the square's side is exactly half the length of the rectangle's longest side. After cutting out the square, it is found that the rectangle's area has been reduced by exactly 38%. The sides of the rectangle and square are all two-digit integers. Find their values.

Read Solution (Total 1)

If x is length and b is breadth of rectangle.
then x/2 is side of square cut from rectangle.

As per given condition

(x/2)^2= 0.38*x*y
x= 0.38*4*y = 1.52y

for x and y to be integer, y can have values 25,50 ( 75 is not possible because in that case x will not be a two digit number)
when y=25
x= 0.38*4*25 =38
then sides of rectangle are 38 and 25 units whereas side of square will be 38/2=19 units

when y=50
x= 0.38*4*50 =76
then sides of rectangle are 76 and 50 units whereas side of square will be 76/2=38 units
12 years agoHelpfull: Yes(1) No(1)

self Other Question

find two integers, neither of which ends in a zero, and whose product is exactly 1,000,000 find 3 consecutive odd integers, all less than 100, such that the sum of their squares forms a Unidigit (that is, all its digits are the same). Thus, for integer abc, a^2 + b^2 +c^2 equals a Unidigital.