1. Знайдіть периметр паралелограма, сторони якого дорівнюють 5 см і 11 см.

2. Один з кутів ромба дорівнює 53°. Знайдіть інші кути ромба.

3. Катети прямокутного трикутника дорівнюють 12 см і 10 см. Знайдіть довжину медіани, проведеної до меншого з катетів.

4. Знайдіть сторони прямокутника, якщо вони відносяться як
2 : 3, а площа прямокутника дорівнює 96 см².

1) Perimeter of the parallelogram = 32 cm

2) The angles of the rhombus include 53°, 53°, 127° and 127°.

3) The length of the median drawn to the smaller of the legs = 13 cm

4) The sides of the rectangle are 8 cm and 12 cm

1) Периметр параллелограмма = 32 см

2) Углы ромба включают 53 °, 53 °, 127 ° и 127 °.

3) Длина медианы обращена к меньшей из ног = 13 см.

4) стороны прямоугольника 8 см и 12 см

Step-by-step explanation:

English Translation

1) Find the perimeter of the parallelogram, the sides of which are 5 cm and 11 cm.

2) One of the angles of the rhombus is 53 °. Find the other angles of the rhombus.

3) The legs of a right triangle are 12 cm and 10 cm. Find the length of the median drawn to the smaller of the legs.

4) Find the sides of the rectangle if they are related as 2: 3, and the area of the rectangle is 96 cm².

Solution

1) Find the perimeter of the parallelogram, the sides of which are 5 cm and 11 cm.

A parallelogram has each of its opposite sides to be equal in length.

Perimeter of a parallelogram = 2(l + b)

l = 11 cm

B = 5 cm

Perimeter = 2(11 + 5) = 32 cm

2) One of the angles of the rhombus is 53 °. Find the other angles of the rhombus.

A rhombus is a quadilateral with the sum of its internal angles equal to 360°. Also, opposite angles of a rhombus are equal in magnitude.

Let the unknown other complementary angle be x.

53° + 53° + x + x = 360°

2x + 106° = 360°

2x = 360° - 106° = 254°

x = (254°/2) = 127°

The angles of the rhombus include 53°, 53°, 127° and 127°.

3) The legs of a right triangle are 12 cm and 10 cm. Find the length of the median drawn to the smaller of the legs.

The median is the line drawn from the vertex opposite a triangle's side to the midpoint of that side.

The median described is drawn in the attached image to this question.

From the image, the small triangle is a right angled triangle, hence, the length of the median is given by Pythagoras theorem.

(Median)² = 12² + 5² = 169

median = 13 cm

4) Find the sides of the rectangle if they are related as 2: 3, and the area of the rectangle is 96 cm².

Let the breadth and length of the rectangle be x and y respectively.

x:y = 2:3

(x/y) =(2/3)

x = (2y/3)

Area of a rectangle = length × breadth = x × y = xy = 96

x = (2y/3)

(2y/3) × y = 96

y² = (96×3/2) = 144

y = 12 cm

x = (2y/3) = (2×12/3) = 8 cm

Hope this Helps!!!

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