Question

Дано: ABCD-ромб, АС и ВD- диагонали, AC=1/2BD, S= 100 см^2, найти диагонали. помогите пожалуйста!!!!!

Answer 1

S=1/2d(1)×d(2) отсюда выразим

Answer 2

Problem Analysis

We are given a rhombus ABCD with diagonals AC and BD. It is known that AC is half the length of BD and the area of the rhombus is 100 cm^2. We need to find the lengths of the diagonals.

Solution

Let's denote the length of AC as x and the length of BD as 2x (since AC is half the length of BD). The area of a rhombus can be calculated using the formula: area = (AC * BD) / 2.

Given that the area is 100 cm^2, we can write the equation as: (x * 2x) / 2 = 100.

Simplifying the equation, we get: x^2 = 100.

Taking the square root of both sides, we find: x = 10.

Therefore, the length of AC is 10 cm and the length of BD is 20 cm.

Answer

The length of the diagonals of the rhombus ABCD are AC = 10 cm and BD = 20 cm.