Geometry Related Problems Line Segment RECTANGLES A rectangle

Geometry Related Problems Line Segment

RECTANGLES § A rectangle is a parallelogram with two pairs of equal opposite sides; and four equal right angles, formed from each pair of adjacent sides which are perpendicular to each other.

ØThe length of a rectangle is 12 cm greater than its width Its perimeter is 60 cm. Find its dimensions.

Ø A rectangle is 10 mm longer than its width and its perimeter is 52 mm. Find the dimensions of the rectangle.

Ø A rectangular field is four times as long as its width. If it were 4 meters shorter and 9 meters wider, its area would be increased by 348 square meters. Find its length and width.

Ø The width of a rectangle is 15 meters and the length is 5 meters shorter than the diagonal. Find the length of the diagonal.

Ø The diagonal of a rectangle is 6 cm longer than its base. Its height is ten cm more than one-third of its base. What are the dimensions of this rectangle?

Practical Applications 18. Last year a native farmer raised sugarcane on a rectangular plot whose length exceeds its width by 9 meters. This year he has increased the width of his plot for sugarcane by five meters and decreased its length by four meters. He has now 70 square meters more allotted to the planting of sugarcane. What is

Ø A man wishes to fence a rectangular lot. If he uses material costing P 1. 50 a meter for the front of the lot and the material costing P 1. 30 a meter for the other three sides, he fence will cost P 380. If he uses the cheaper material for all four sides of the lot the fence will cost P 364. Find the dimensions

Ø Within a rectangular garden 15 meters wide and 25 meters long, we wish to pave a walk around the borders of uniform width whose area is 144 square meters for violets. How wide should the walk be?

Ø A rectangular flower plot has an area of 1, 728 square meters and is surrounded by a path 2 meters wide. The area of the path is 320 square meters. Find the length and width of the flower plot.

Ø The area of the page of a book is 88 square cm, the area of the printed part is 51 square cm. The margin at the top and sides is 1 cm wide, and the margin at the bottom is 1 ½ cm wide. Find the dimensions of the page.

Ø A rectangular sheet of cardboard is twice as long as it is wide. An open box case having a capacity of 648 cubic cm is made by cutting 3 cm squares from the corners and the bending up the sides and ends. Find the dimensions of the cardboard.

The square § A square is a rectangle all of whose sides are equal and consist of four right angles formed from the pair of adjacent sides.

Measurements Ø The perimeter of a square is equal to four times the length of one of its sides or edge as it is often called Perimeter of Square = 4 times length of Side The area of a square is equal to the square of the length of one of its side:

Ø The side of one square is 3 centimeters longer than twice the length of the side of the second square, and the difference in the area of the square is 105 square centimeters. Find the length of the side of the square.

A food tray with a square base and a volume of 675 cubic cm is to be constructed from a square sheet of tin by cutting 3 cm squares from the corners and bending up the sides. What size sheet of tin should be used for the purpose?

The Circle § Definition & Properties A circle is a set of points equidistant from a common point called the center. § Parts of a Circle The parts of a circle consist of its center and radius. The radius is the line segment whose endpoints are the center of the circle and any point on the circle.

Measurements § The circumference of a circle is its perimeter calculated by multiplying twice the product of π and the radius § The area of a circle is the total amount of planar space enclosed within the circumference of the circle and is obtained by multiplying the constant by the square of the length of the radius

ØTwo coins are tangent to a third coin internally and are tangent to each other externally. The distances between their centers are 14 mm, 7 mm, 5 mm. Find their radii.

ØA circular rose bed is bordered by a 4 meter walk. The area planted is 9/16 of the area of the bed. What is the radius of the bed.