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In this lesson, we will learn how to write and simplify ratios and how to use that to solve problems in geometric context.

Q1:

Find, in the simplest form, the ratio between the circumference of a circle whose radius is 63 cm and the perimeter of a square whose side length is 7 cm, where 𝜋 = 2 2 7 .

Q2:

Using the figures, determine the ratio between the area of triangle 𝐴 𝐵 𝐶 and the area of square 𝑋 𝑌 𝑍 𝐿 . Give your answer in its simplest form.

Q3:

Given that the area of a triangle is 52 cm^{2}, and its base length is 13 cm, determine the ratio between its base length and its height.

Q4:

Express the ratio 7 . 4 4 8 0 0 1 2 . 6 k m : m : k m in its simplest form.

Q5:

A triangle has side lengths 5 cm, 12 cm, and 13 cm. A rhombus has side length 0.71 m. Express the ratio of the perimeters of the triangle and the rhombus in its simplest form.

Q6:

Express the following ratio in its simplest form: 1 2 ∶ 2 3 7 5 L m L .

Q7:

In the figure below, what is the ratio between the green parts and red parts in its simplest form?

Q8:

If the side length of a square is equal to the side length of an equilateral triangle, what is the ratio of the perimeter of the square to the perimeter of the equaliteral triangle?

Q9:

The area of a rectangle is 210 cm^{2}, and its width is 10 cm. What is the ratio between the length and perimeter of the rectangle in its simplest form?

Q10:

Find the ratio between the lengths and in its simplest form.

Q11:

A parallelogram has a base length of 79 mm and corresponding height of 18 mm. A rhombus has diagonal lengths of 4.6 cm and 3.7 cm. Find the ratio of the area of the parallelogram to that of the rhombus.

Q12:

Square A has a side length of 6 𝑥 cm. Square B has a side length of 7 𝑥 cm. What is the ratio of the areas of squares A and B in its simplest form?

Q13:

Find the ratio between the perimeter of the rhombus and the circumference of the circle in its simplest form using 𝜋 = 2 2 7 .

Q14:

The length of the diagonal in a square is 22 cm. A parallelogram has a base length of 25 cm and perpendicular height of 10 cm. What is the ratio between the areas of the square and the parallelogram in its simplest form?

Q15:

Determine the ratio between the quantities 2 4 ∶ 2 8 0 ∶ 2 . 2 d m c m m in the simplest form.

Q16:

A square has side length 12 cm and a rectangle has sides of length 20 cm and 6 cm. What is the ratio between the perimeter of the rectangle and that of the square in its simplest form?

Q17:

In a given rectangle, the length is four times the width. If the length is 40 cm, express the ratio between the rectangle’s perimeter and length in its simplest form.

Q18:

A square has a perimeter of 1.6 m. A rectangle has a width of 15 cm, and its length exceeds the side length of the square by 21 cm. Express the ratio of the area of the square to the area of the rectangle in its simplest form.

Q19:

A piece of wire, which is 120 cm, was divided into two parts with a ratio of 1 1 ∶ 4 . A circle was shaped from the long part, and a square was shaped from the short one. Determine the ratio between the area of the square and that of the circle in its simplest form. 𝜋 = 2 2 7 .

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