Question

Одна из диагоналей ромба на 4 см больше другой, а площадь равна 96 см квадратных.Найти стороны ромба. Пожалуйста, полное решение без дискриминанта (его ещё не проходили).

Answer 1

Без дискриминанта это не решить

Answer 2

Problem Analysis

We are given that one of the diagonals of a rhombus is 4 cm longer than the other diagonal, and the area of the rhombus is 96 square cm. We need to find the lengths of the sides of the rhombus.

Solution

Let's assume that the length of the shorter diagonal is x cm. Then the length of the longer diagonal is x + 4 cm.

The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2.

Substituting the given values, we have: 96 = (x * (x + 4)) / 2.

To solve this equation, we can multiply both sides by 2 to eliminate the fraction: 192 = x^2 + 4x.

Rearranging the equation, we get: x^2 + 4x - 192 = 0.

To solve this quadratic equation, we can factor it or use the quadratic formula. Since we want to avoid using the discriminant, let's factor the equation.

Factoring the equation, we have: (x - 12)(x + 16) = 0.

Setting each factor equal to zero, we get two possible solutions: x - 12 = 0 or x + 16 = 0.

Solving for x, we find two possible values: x = 12 or x = -16.

Since the length of a side cannot be negative, we discard the solution x = -16.

Therefore, the length of the shorter diagonal is x = 12 cm, and the length of the longer diagonal is x + 4 = 16 cm.

In a rhombus, all sides are equal in length. So, the lengths of the sides of the rhombus are 12 cm and 16 cm.

Answer

The lengths of the sides of the rhombus are 12 cm and 16 cm.