Question

диагонали ромба относятся как 8 : 15 а его площадь равна 240 см в квадрате найдите диагонали ромба

Answer 1

1- я диагоноль это 8 x вторая 15 x . 
площаь ромба=(8х*15х)/2=240 

х=2 
диагональ 1=8*2=16 
диагональ2=15*2=30

Answer 2

Finding the Diagonals of a Rhombus

To find the diagonals of a rhombus when the ratio of the diagonals is given as 8:15 and the area of the rhombus is 240 cm², we can use the following steps:

1. Calculate the Lengths of the Diagonals: - Let's assume the lengths of the diagonals are 8x and 15x, where x is a common factor. - The area of a rhombus can be calculated using the formula: Area = (1/2) * d1 * d2, where d1 and d2 are the lengths of the diagonals. - We can use the given area to find the value of x and then calculate the lengths of the diagonals.

2. Use the Given Area to Find the Value of x: - The area of the rhombus is given as 240 cm². - We can use the area formula to find the value of x and then calculate the lengths of the diagonals.

3. Calculate the Lengths of the Diagonals: - Once we have the value of x, we can calculate the lengths of the diagonals using the ratio 8:15.

Let's proceed with the calculations based on the given information.

Calculations

Using the formula for the area of a rhombus, we can find the value of x:

Area = (1/2) * d1 * d2 240 = (1/2) * 8x * 15x 240 = 60x² x² = 240 / 60 x² = 4 x = √4 x = 2

Now that we have the value of x, we can calculate the lengths of the diagonals: - Length of the first diagonal (d1) = 8x = 8 * 2 = 16 cm - Length of the second diagonal (d2) = 15x = 15 * 2 = 30 cm

So, the lengths of the diagonals of the rhombus are: - The first diagonal (d1): 16 cm - The second diagonal (d2): 30 cm

Therefore, the lengths of the diagonals of the rhombus are 16 cm and 30 cm.

This calculation is based on the given area and the ratio of the diagonals, and it provides the lengths of the diagonals of the rhombus.