The area of the rhombus is 24 cm2, and the lengths of its diagonals are 3: 4. Find the length of the side of the rhombus.

| November 22, 2020 | education

Given a rhombus ABCD, the diagonals AC and BD intersect at point O. S (ABCD) = 1/2 * AC * BD = 24cm ^ 2. By condition AC: BD = 3: 4. Let’s introduce the variable x = 1 part => BD = 4x, AC = 3x. We substitute the rhombus area into the formula and an incomplete quadratic equation is obtained: 1/2 * 3x * 4x = 24 12x ^ 2 = 12 x ^ 2 = 1 => x = 1 => BD = 4, AC = 3. Consider a triangle ABO – rectangular (since the diagonals in the rhombus intersect at right angles). By the property of a rhombus (the diagonals are divided by the intersection point in half at the intersection) VO = DO = 4/2 = 2 cm AC = CO = 3/2 = 1.5 cm. Triangle ABO – rectangular => according to the Pythagorean theorem AB ^ 2 = BO ^ 2 + AO ^ 2 = 2 ^ 2 + 1.5 ^ 2 = 4 + 2.25 = 6.25 => AB = 2.5. And in a rhombus, all sides are equal.
Answer: rhombus side = 2.5.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.