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Geometry
1. A rhombus has diagonals of 32 and 20 inches. Find the area and the angle opposite the longer diagonal.
2. If the diagonal length of a square is tripled, how much is the increase in the perimeter of that square?
3. The area of the rhombus is 156 m^2. If it's shorter diagonal is 13 meters, find the length of the longer diagonal.
4. The altitude BE of a parallelogram ABCD divides the side AD into segments in the ratio 1 is to 3. Find the area of the parallelogram if the length of its shorter side is 14 cm, and one of its interior angle measures 60 degrees.
5. The vertical end of a trough, which is in the form of a trapezoid, has the following dimensions: width at the top is 1.65 meters, width at the bottom is 1.15 meters, and depth is 1.35 meters. Find the area of this section of the trough.
2. If the diagonal length of a square is tripled, how much is the increase in the perimeter of that square?
3. The area of the rhombus is 156 m^2. If it's shorter diagonal is 13 meters, find the length of the longer diagonal.
4. The altitude BE of a parallelogram ABCD divides the side AD into segments in the ratio 1 is to 3. Find the area of the parallelogram if the length of its shorter side is 14 cm, and one of its interior angle measures 60 degrees.
5. The vertical end of a trough, which is in the form of a trapezoid, has the following dimensions: width at the top is 1.65 meters, width at the bottom is 1.15 meters, and depth is 1.35 meters. Find the area of this section of the trough.
Geometry
1. An isosceles trapezoid has an area of 40 m^2 and an altitude of 2 meters. Its two bases have a ratio of 2 is to 3. What are the lengths of the bases and one diagonal of the trapezoid?
2. A piece of wire of length 52 meters is cut into two parts. Each part is then bent to form a square. It is found that the combined area of the two squares is 109 m^2. Find the measure of the sides of the two squares.
2. A piece of wire of length 52 meters is cut into two parts. Each part is then bent to form a square. It is found that the combined area of the two squares is 109 m^2. Find the measure of the sides of the two squares.
Geometry
1. Find the height of a parallelogram with 10 sides and 20 inches long, and an included angle of 35 degrees. Also, calculate the area of the figure.
2. A certain city block is in the form of a parallelogram. Two of its sides measures 32 ft and 41 ft. If the area of the land in the block is 656 ft^2, what is the length of its longer diagonal?
3. The area of an isosceles trapezoid is 246 m^2. If the height and the length of one of its congruent sides measures 6m and 10m, respectively, find the length of the two bases.
2. A certain city block is in the form of a parallelogram. Two of its sides measures 32 ft and 41 ft. If the area of the land in the block is 656 ft^2, what is the length of its longer diagonal?
3. The area of an isosceles trapezoid is 246 m^2. If the height and the length of one of its congruent sides measures 6m and 10m, respectively, find the length of the two bases.
Geometry
P & Q are the points of contact of the tangents drawn from the point T to the parabola y2 = 4ax. If PQ be the normal to the parabola at P, prove that TP is bisected by the directrix.
Geometry
O' is the vertex of the parabola y2 = 4ax & L is the upper end of the latus rectum. If LH is drawn perpendicular to OL meeting OX in H, prove that the length of the double ordinate through H is 4a(root)5
Geometry
Determine the range of values of θ ∈ [0, 2 π] for which the point (cos θ, sin θ) lies inside the triangle formed by the lines x + y = 2 ; x − y = 1 & 6x + 2y − 10 = 0.
Geometry
Determine all values of α for which the point (α, α²) lies inside the triangle formed by the lines 2x + 3y − 1 = 0 ; x + 2y − 3 = 0 ; 5x − 6y − 1 = 0.
Geometry
Consider the family of lines, 5x + 3y − 2 + K1 (3x − y − 4) = 0 and x − y + 1 + K2(2x − y − 2)=0. Find the equation of the line belonging to both the families without determining their vertices.
Geometry
1. In a right triangle, the bisector of the right angle divides the hypotenuse in the ratio of 3:5. Determine the measures of the acute angles of the triangle.
2. The lengths of the sides of a triangle are in the ratio of 17:10:9. Find the lengths of the three sides if the area of the triangle is 576cm^2.
3. In an acute triangle ABC, an altitude AD is drawn. Find the area of triangle ABC if AB = 15 inches, AC = 18 inches and BD = 10 inches.
4. Given triangle ABC whose sides are AB = 15 inches, AC = 25 inches and BC = 30 inches. From a point D on side AB, a line DE is drawn to a point E on side AC such that angle ADE is equal to angle ABC. If the perimeter of triangle ADE is 28 inches. Find the lengths of line segments BD and CE.
2. The lengths of the sides of a triangle are in the ratio of 17:10:9. Find the lengths of the three sides if the area of the triangle is 576cm^2.
3. In an acute triangle ABC, an altitude AD is drawn. Find the area of triangle ABC if AB = 15 inches, AC = 18 inches and BD = 10 inches.
4. Given triangle ABC whose sides are AB = 15 inches, AC = 25 inches and BC = 30 inches. From a point D on side AB, a line DE is drawn to a point E on side AC such that angle ADE is equal to angle ABC. If the perimeter of triangle ADE is 28 inches. Find the lengths of line segments BD and CE.
Geometry
1. Find the area of a triangle if its two side measure 6 inches and 9 inches, and the bisector of the angle between the sides is 4 square root of 3 inches.
2. In a right triangle, a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hypotenuse into segments which are 10 cm and 6 cm long. Find the lengths of the two sides of the triangle.
3. The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18 cm and 15 cm, respectively. Find the lengths of the sides of the triangle.
2. In a right triangle, a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hypotenuse into segments which are 10 cm and 6 cm long. Find the lengths of the two sides of the triangle.
3. The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18 cm and 15 cm, respectively. Find the lengths of the sides of the triangle.
