Math Problem Statement

Multiple mathematics questions, including parallelogram perimeter, triangle area, distance between points, and more.

Solution

I see that you have uploaded a photo containing several mathematics problems. I'll help you solve them step by step. Here is a summary of the questions:

Questions in the Image:

  1. Perimeter and ratio of sides of a parallelogram.
  2. Area and perimeter of a right triangle.
  3. Area of a triangle using side lengths.
  4. Area and perimeter difference for a square.
  5. Value of the smallest angle in a right-angled triangle.
  6. Length of a side in a right triangle.
  7. Area of an isosceles triangle.
  8. Area of a right triangle.
  9. Distance between two points.
  10. Midpoint between two points.
  11. Distance between a point and origin.
  12. Equation of a straight line.
  13. Equation of a line passing through a point.
  14. Measure the area of a given shape.
  15. Area of a quadrilateral formed by four points.
  16. Values of a parameter such that points lie on a straight line.
  17. Points on a straight line with given slope.
  18. Perimeter and diagonal of a rectangle.
  19. Area of a triangle using diagonals.
  20. Perimeter of a rhombus.
  21. Length of a side of a triangle.

Let's begin solving these problems one by one. Please let me know if you'd like to start with a specific question or go in order.

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Trigonometry
Coordinate Geometry

Formulas

Perimeter of parallelogram: P = 2(a + b)
Area of triangle: A = (1/2) * base * height
Distance between two points: d = √((x2 - x1)^2 + (y2 - y1)^2)
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Pythagorean theorem: a^2 + b^2 = c^2

Theorems

Pythagorean theorem
Basic trigonometric identity
Distance and midpoint theorems in coordinate geometry

Suitable Grade Level

Grades 8-10