Quadratic equation + rectangle - practice problems
Number of problems found: 62
- Width and length
For a particular rectangle, twice the width is 1 meter longer than the length. The area of the rectangle is 153 square meters. What is the perimeter of the rectangle? - The area 3
The area of a rectangle is given by the expression 4x² + 5x -6. What is the length of the rectangle if its width is x+2? - Vertex of the rectangle
Determine the coordinates of the vertex of the rectangle inscribed in the circle x²+y² -2x-4y-20=0 if you know that one of its sides lies on the line p: x+2y=0 - Calculated 82619
When modifying the school plot in the shape of a rectangle, the deviation was calculated if we increased the length and width of the plot by 1m and its area by 22 m². If we reduce the length of the plot by 2m and increase its width by 1m, its area will de
- Rectangle 79084
A rectangle whose one side measures 35m and the other is 7m shorter than the diagonal of the rectangle. Calculate the content in m². - Rectangle 78924
The length of the rectangle is 1 cm more than its width. Its content is 4 cm². What is its width? - A yard
Yevgen is fencing in a yard that is 30 meters longer than it is wide. The yard will have an area of 1000 m². Find its width and length. - The length 11
The length of a rectangle is four times its width. If the area is 100 m², what is the length of the rectangle? - One side 2
One side of the rectangle is three times larger, and the other is 4 cm smaller than the side of the square. Find the area of the square if more than the area of the rectangle by 10 cm².
- An equivalent
An equilateral triangle has the same perimeter as a rectangle whose sides are b and h (b > h). Considering that the area of the triangle is three times the area of the rectangle. What is the value of b/h? - The width
The width of a rectangular garden is 4 m less than the length. If the area of a rectangular garden is 96 square meters, what is the garden's dimension? - Two gardens
The flower garden has a square shape. The new garden has a rectangular shape; one dimension is 8 m smaller, and the other is twice as large as in a square garden. What were the original and new garden dimensions if both gardens' areas were the same? - A rectangle 4
A rectangle has an area of 300 and a perimeter of 80. What is the ratio of length and width? - The pool
The cube-shaped pool has 140 cubic meters of water. Determine the bottom's dimensions if the water's depth is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom?
- How many
How many different rectangles with integer side lengths have an area S = 60 cm²? - Area and perimeter of rectangle
The rectangle area is 3000 cm2, and one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle. - Perimeter and diagonal
The perimeter of the rectangle is 82 m, and the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Circumference 26651
A rectangle with sides of lengths a, b (cm) has a circumference of 100 cm. The dependence of its area P (in cm2) on the number a can be expressed by the quadratic function P = sa + ta². Find the coefficients s, t. - A map
A map with a scale of 1:5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field?
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