PKN wrote:

Bunuel wrote:

If a wooden slab with dimensions 6 x 6.5 can be cut to form a rectangle with sides of integer lengths, what is the area of the largest such rectangle that can be formed?

A. 36

B. 30

C. 25

D. 20

E. 16

Note:

1) A rectangle with four sides of equal length is a square. Or, So a square is a special kind of rectangle.NOT EVERY RECTANGLE IS A SQUARE.

2) if a rectangle and a square have the same perimeter, the rectangle must have a smaller area than the square

So, area of the rectangle will be the largest when we cut it in such a way that it bears the largest length making a square.

Hence, Length of square would be =6 unit

Therefore, \(area=6^2=36\)

Ans. (A)

+1 for (A)

A square is a special kind of rectangle, it is one where all the sides have the same length.

All the properties (Except Length of sides ) applicable to a Rectangle is applicable for a Square & Rectangle are as follows -

Square. Its properties are(a) All sides are equal.

(b) Opposite sides are equal and parallel.

(c) All angles are equal to 90 degrees.

(d) The diagonals are equal.

(e) Diagonals bisect each other at right angles.

(f) Diagonals bisect the angles.

(g) The intersection of the diagonals is the circumcentre. That is, you can draw a circle with that as centre to pass through the four corners.

(h) The intersection of the diagonals is also the incentre. That is, you can draw a circle with that as centre to touch all the four sides.

(i) Any two adjacent angles add up to 180 degrees.

(j) Each diagonal divides the square into two congruent isosceles right-angled triangles.

(k) The sum of the four exterior angles is 4 right angles.

(l) The sum of the four interior angles is 4 right angles.

(m) Lines joining the mid points of the sides of a square in an order form another square of area half that of the original square.

(n) Join the quarter points of a diagonal to the vertices on either side of the diagonal and you get a rhombus of half the area of the original square.

(o) Revolve a square about one side as the axis of rotation and you get a cylinder whose diameter is twice the height.

(p) Revolve a square about a line joining the midpoints of opposite sides as the axis of rotation and you get a cylinder whose diameter is the same as the height.

(q) Revolve a square about a diagonal as the axis of rotation and you get a double cone attached to the base whose maximum diameter is the same as the height of the double cone.

Rectangle. Its properties are

(a) Opposite sides are equal and parallel.

(b) All angles are equal to 90 degrees.

(c) The diagonals are equal and bisect each other.

(d) The intersection of the diagonals is the circumcentre. That is you can draw a circle with that as centre to pass through the four corners.

(e) Any two adjacent angles add up to 180 degrees.

(f) Lines joining the mid points of the sides of a rectangle in an order form a rhombus of half the area of the rectangle.

(g) The sum of the four exterior angles is 4 right angles.

(h) The sum of the four interior angles is 4 right angles.

(i) Join the opposite sides of a rectangle and you get four congruent rectangles of one-fourth the size of the main rectangle.

(j) Join the midpoints of the sides in order and you get a parallelogram whose sides are parallel to the diagonals.

(k) Revolve a rectangle about the longer side as the axis of rotation and you get a cylinder whose diameter is twice the width of the rectangle and the height same as the length of the rectangle.

(l) Revolve a rectangle about the shorter side as the axis of rotation and you get a cylinder whose diameter is twice the length of the rectangle and the height same as the width of the rectangle.

(m) Revolve a rectangle about a line joining the midpoints of opposite longer sides as the axis of rotation and you get a cylinder whose diameter is the same as the length of the rectangle and its height as the width of the rectangle.

(n) Revolve a rectangle about a line joining the midpoints of opposite shorter sides as the axis of rotation and you get a cylinder whose diameter is the same as the width of the rectangle and its height as the length of the rectangle.

(o) Revolve a rectangle about a diagonal as the axis of rotation and you get a solid with two cones at the ends of the axis with the slant heights same as the width of the rectangle separated by two frustums of cones attached at their smaller ends.

Answer must be (A)
_________________