# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.- Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. - Calculate

Calculate the length of a side of the equilateral triangle with an area of 50cm^{2}. - Equilateral triangle

Calculate the area of an equilateral triangle with circumference 72cm. - Rhombus 29

One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus. - Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Map scale

The rectangular plot has in a scale of 1: 10000 area 3 cm^{2}on the map. What content does this plot have on a 1:5000 scale map? - Painters

Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours? - A rectangular

A rectangular garden 40 m long and 30 m wide is to be fenced with fence posts at each corner. All the other posts will be 5 meters a part. How many posts will be needed to fence in the garden. - Perimeter of a rectangle

If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width? - Three points 2

The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. - Complementary angles 2

Two complementary angles are (x+4) and (2x - 7) find the value of x - Ruler and compass

Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°. - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Coordinate axes

Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y. - Construct

Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long. - Trapezoid - intersection of diagonals

In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area. - Table

Find the circumference of the table, where the long side is 1.28 meters and the short side is 86 cm. - Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm^{2}. Calculate content of square over the triangle's hypotenuse. - Rectangle area

The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?

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