Math Problem Statement

One of the diagonals of a rhombus is 48cm long and the length of each side of the rhombus is 26cm. Find the length of the other diagonal and and also find the area of the rhombus. with diagram

Solution

Here is the diagram of the rhombus, showing the diagonals and the right-angled intersection. The length of one diagonal is 48 cm, and the other diagonal, which we calculated, is 20 cm. The side of the rhombus is 26 cm.

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Related questions:

  1. How can we use the properties of a rhombus to prove the diagonals bisect at right angles?
  2. What other methods can be used to calculate the area of a rhombus?
  3. How do the diagonals of a rhombus relate to its symmetry?
  4. If the diagonals were of equal length, what would the shape of the rhombus be?
  5. How would you find the angles of a rhombus given the side length and diagonals?

Tip: In geometric problems involving rhombuses, remember that diagonals bisect each other at right angles, and this property is often useful in applying the Pythagorean theorem.

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Math Problem Analysis

Mathematical Concepts

Geometry
Rhombus Properties
Pythagorean Theorem

Formulas

Area of rhombus = (d1 * d2) / 2
Pythagorean Theorem: a^2 + b^2 = c^2

Theorems

Properties of rhombus
Diagonals bisect at right angles

Suitable Grade Level

Grades 8-10