Question

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

Answer 1

S=30*16/2=240
Точка пересечения диагоналей делит ромб на 4 прямоугольных треугольника с катетами 15 и 8,найдем гипотенузу, которая и является стороной ромба
По теореме Пифагора
225+64=а^2
а=17

Answer 2

Площадь = 0,5 произведения диагоналей

S=0,5 * 16 * 30 = 240 кв.см

диагонали в точке пересечения делятся пополам, боковая сторона по теореме Пифагора:

a=√(15^2 + 8^2) = √(225 + 64) = √289 = 17 см

Answer 3

Finding the Side and Area of a Rhombus with Given Diagonals

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

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

2. Finding the Area of the Rhombus: - The area of the rhombus can be calculated using the formula: A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

Calculation

Using the given diagonals: - d1 = 30 cm - d2 = 16 cm

1. Finding the Side of the Rhombus: - Using the formula: s = sqrt((30/2)^2 + (16/2)^2) - Calculating: s = sqrt(225 + 64) - Therefore, s = sqrt(289) - Hence, s = 17 cm.

2. Finding the Area of the Rhombus: - Using the formula: A = (30 * 16) / 2 - Calculating: A = 240 / 2 - Therefore, A = 120 sq cm.

So, the side of the rhombus is 17 cm and the area of the rhombus is 120 sq cm.

These calculations are based on the provided formulas and the given lengths of the diagonals.