Perimeter And A...

Rectangular tiles each of size 70 cm 30 cm must be laid horizontally on a rectangular floor of size 110 cm 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. What is the maximum number of tiles that can be accommodated on the floor?

The sides of a rectangular park are in the ratio 3 : 2 and its area is 3,750 m². The cost of fencing it at 50 paisa per metre is:

From a circular sheet of paper with radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

The figure shows rectangle ABCD with a semicircle and a circle inscribed in it. What is the ratio of the area of the circle to that of the semicircle?

Two sides of a plot measure 32 m and 24 m, and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles.



What is the area of the plot (in m²)?

In a triangle ABC, the lengths of the sides AB and AC are 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

The diameter of a wheel is 63 cm. Distance travelled by the wheel in 100 revolutions is:

The sides of a square are increased by 20% and 40%, respectively. The area of the resulting rectangle exceeds the area of the square by:

Two circles, both of radii 1 cm, intersect such that the circumference of each one of them passes through the centre of the other. What is the area (in sq cm) of the intersecting region?

A jogging park has two identical circular tracks touching each other and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?

A square tin sheet of side 12 inches is converted into a box with open top in the following steps-The sheet is placed horizontally. Equal sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?

Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder.

The length of a rectangular field is 50% more than its breadth. If the total cost of fencing the field at the rate of Rs. 60 per metre is Rs. 12,000, what is the length of that field?

A rectangular plank m wide is placed symmetrically on the diagonal of a square of side 8 m as shown in the figure.



The area of the plank is:

The length of the circumference of a circle is equal to the perimeter of a triangle of equal sides and also the perimeter of a square. The areas covered by the circle, triangle and square are c, t and s, respectively. Choose the most appropriate option.

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the longer to the shorter side?

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach another. There is a small circular pond of area 20m² at the centre. How much area is left ungrazed?

P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is diameter of the circle. What is the perimeter of the quadrilateral PQSR?

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m² at the centre. Find the ungrazed area.

The diagonal of square A is (a + b). Find the diagonal of square B, whose area is twice the area of A.