# 6.1.3. Miscellaneous Exercises on Ratio and Its Properties

is a rectangle in which cm, and is a square whose side length is cm, where . Find the length of and the perimeter of the shaded part.

• Acm, cm
• Bcm, cm
• Ccm, cm
• Dcm, cm
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The ratio of the age of a father to that of his child is . If the child is 7 years old, how old is his father?

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The ratio of the age of a father to that of his child is . If the child is 8 years old, how old is his father?

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The ratio between the areas of two pieces of lands is . If the area of land A exceeds that of land B by , find the area of land B.

• A
• B
• C
• D
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The ratio between the areas of two pieces of lands is . If the area of land A exceeds that of land B by , find the area of land B.

• A
• B
• C
• D
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The ratio between Mahmoud's money and Amr's money is . If the sum of their money is LE, how much money does Mahmoud have?

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The ratio between Ayman's money and Aya's money is . If the sum of their money is LE, how much money does Ayman have?

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Determine the area of a rectangle whose perimeter is cm, given that the ratio between its dimensions is .

• A
• B
• C
• D
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Determine the area of a rectangle whose perimeter is cm, given that the ratio between its dimensions is .

• A
• B
• C
• D
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If the ratio between Ahmed’s and Omar’s height is , where Omar is cm, find Ahmed's height.

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If the number of pupils in the sixth grade in a school is 203, and the ratio between the number of boys to girls is , find the number of each of boys and girls in this grade.

• A87, 116
• B152, 116
• C87, 270
• D152, 270
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Find the two numbers whose sum is 243, and the ratio between them is .

• A81, 486
• B121, 486
• C121, 162
• D81, 162
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If a piece of land was divided between two persons according to the ratio , where the share of the first person exceeds that of the second one by 81 square metres, find the area of the piece of the land.

• A
• B
• C
• D
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If the ratio between the heights of two buildings in a town is , where the difference between their heights is 8 meters, find the height of each of them.

• Am, m
• Bm, m
• Cm, m
• Dm, m
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Two persons started a food business, where the ratio between what the first paid and what the second paid is . Given that the second person paid LE more than the first, determine the capital of the business.

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In a football league, the ratio between the number of goals of a team and the number of goals of another team is , where the sum of their goals is 66, find the number of goals of each team.

• A30 goals, 79 goals
• B55 goals, 79 goals
• C30 goals, 36 goals
• D55 goals, 36 goals
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Determine the length and the width of the rectangular piece of land whose perimeter is m, given that the ratio between them is .

• A474, 632
• B316, 632
• C316,
1 896
• D474,
1 896
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If and , then .

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In the figure below, is a rectangle, where cm, and is a square of side length cm, where . Determine the ratio between the area of the square and that of the rectangle in the simplest form, and then find the area of the shaded part.

• A,
• B,
• C,
• D,
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A wire that has a length of cm has been divided with the ratio to design the square and equilateral triangle shown below respectively. Determine the values of and .

• A,
• B,
• C,
• D,
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