Question

Найдите сторону и площадь ромба,если его диагонали равны 30 и 16 см.

Answer 1

Площадь ромба равна половине произведения его диагоналей:
S = 1/2•30см•16см = 240 см²
Диагонали точкой пересечения делятся пополам, поэтому одна диагональ разделиться на отрезки 15 см и 15 см, а другая - на 8 и 8 см.
Угол между диагоналями равен 90°, поэтому, используя теорему Пифагора найдём сторону:
√15² + 8² = √225 + 64 = √289 = 17.
Ответ: 240 см², 17 см.

Answer 2

Finding the Side and Area of a Rhombus

To find the side and area of a rhombus when its diagonals are given as 30 cm and 16 cm, we can use the following formulas:

1. Finding the Side (s) of the Rhombus: - The side of a rhombus can be calculated using the formula: \( s = \sqrt{\frac{d1^2 + d2^2}{4}} \), where \( d1 \) and \( d2 \) are the lengths of the diagonals.

2. Finding the Area (A) of the Rhombus: - The area of a rhombus can be calculated using the formula: \( A = \frac{d1 \times d2}{2} \), where \( d1 \) and \( d2 \) are the lengths of the diagonals.

Calculations

1. Finding the Side (s) of the Rhombus: - Using the given diagonals \( d1 = 30 \) cm and \( d2 = 16 \) cm: - \( s = \sqrt{\frac{30^2 + 16^2}{4}} \) - \( s = \sqrt{\frac{900 + 256}{4}} \) - \( s = \sqrt{\frac{1156}{4}} \) - \( s = \sqrt{289} \) - \( s = 17 \) cm

- The side of the rhombus is 17 cm.

2. Finding the Area (A) of the Rhombus: - Using the given diagonals \( d1 = 30 \) cm and \( d2 = 16 \) cm: - \( A = \frac{30 \times 16}{2} \) - \( A = \frac{480}{2} \) - \( A = 240 \) sq. cm

- The area of the rhombus is 240 sq. cm.

Therefore, the side of the rhombus is 17 cm and the area of the rhombus is 240 sq. cm.