Planimetry - math word problems - page 87 of 187
Number of problems found: 3739
- Republic
First, guess which circle has the larger diameter: the one with the same area as the area of the Czech Republic, or the one with a circumference equal to the length of the border of the Czech Republic? Then check your guess by calculating. The area of the - Broken tree
The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top, but does not fall off. It is refuted on the ground. How far from the base of the tree lay its peak? - Triangle hypotenuse circle
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle. - Mast rope anchoring
The mast is 190 m high and is attached to six ropes which are anchored in the ground at a distance of 20 m from the base of the mast. How many meters of rope were needed? - Circle chord distance
The figure shows the circles k₁(S₁; r1=9 cm) and k₂(S2; r2 = 5 cm). Their intersections determine a common chord t 8 cm long. Calculate the center distance |S₁ S₂| in cm to two decimal places. - Clock hand distance
How far apart are the tips of the clock's hands in 3 hours if the larger hand is 124 mm long and the smaller 75 mm? - Right 24
The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse, dividing it into two unequal segments. One segment is 5 cm long. What is the area of the triangle? Thank you. - Triangle KLM
In the rectangular triangle KLM, where |KL|=m is the hypotenuse (sketch it!). Find the length of the leg k and the height of triangle h if the hypotenuse's segments are known MK = 5 cm and ml = 15 cm. - Paper squares
We need to cut a paper rectangle measuring 69 cm by 46 cm into the largest possible identical squares. Calculate the side length of the squares and their number. - Infinity
A square with a side 19 long is an inscribed circle, and the circle is inscribed next to the square, circle, and so on to infinity. Calculate the sum of the area of all these squares. - Pagans
Elena cut out the same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagan occupied 28.26 cm² of the bottom of the sh - Circle's chords
The circle has two chord lengths, 30 and 34 cm. The shorter chord is twice as far from the center as the longer one. Determine the radius of the circle. - IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm. - Right triangle generator
Detective Harry Thomson found on the Internet a generator for the side lengths of right triangles. According to it: a = 2xy, b = x² − y², c = x² + y², where x and y are natural numbers and x > y. Is it a working generator? - Tablecloth diameter calculation
The round tabletop has a capacity of 2.01 m². Calculate the diameter of the round tablecloth if it exceeds the table's edge by 25 cm. - Square and circles
The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a. - Office Carpet and Rails
The worker bought a new carpet with moldings for the square office. The rails for this office cost CZK 1,500; 15 CZK per 1 m. How many m² does this office, in which six people work? - Right triangle area
In a right-angled triangle ABC, the height of side c has a length of 6 cm. The letter D indicates the heel of the height. Line segment AD is 8 cm long. Calculate the area of triangle ABC. ( example on Monitor 9 ) - Tiles
The hall has dimensions 250 × 200 dm. What is the largest size of square tiles that can be tiled throughout the hall, and how many do we need? - RT = legs, circle
One leg of a right triangle ABC has length a= 14 cm and the radius of the circle inscribed in this triangle r= 5 cm. Calculate the length of the hypotenuse and its other leg.
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