Question

Найти площадь ромба если разность диагоналей равно 10см, а сторона 25см.

Answer 1

Диагональ1=2х
диагональ2=2х+10
диагонали в ромбе делятся пополам, и пересекаются под углом 90
в прямоугольном треугольнике половины диагоналей=катетам, сторона ромба=гипотенузе,
х в квадрате + (х+5) в квадрате = 25*25
х в квадрате+х в квадрате + 10х + 25 = 625
х в квадрате + 5х - 300 = 0
х = (-5 +- корень(25 + 4*300)) / 2
х=15
диагональ1= 15*2=30
диагональ2=30+10=40
площадь ромба= (диагональ1 * диагональ2) / 2 = (30*40)/2=600

Answer 2

Finding the Area of a Rhombus

To find the area of a rhombus, we can use the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals of the rhombus.

Given: - The difference between the diagonals, d1 - d2 = 10 cm - The length of a side, s = 25 cm

Calculating the Area

Using the given information, we can calculate the area of the rhombus.

First, let's find the lengths of the diagonals: - Since the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the lengths of the diagonals.

Let's denote: - d1 as the longer diagonal - d2 as the shorter diagonal

Using the Pythagorean theorem: - d1^2 = (s/2)^2 + (s/2)^2 - d2^2 = s^2 - d1^2

After finding the lengths of the diagonals, we can calculate the area using the formula mentioned earlier.

Conclusion

By using the given information and the formula for the area of a rhombus, we can calculate the area of the given rhombus.