Question icon
12 grade maths others

In a rectangle, the difference between the sum of adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

A. √3 : 2
B. 1 : √3
C. 2 : 5
D. 3 : 4

Profile image of Aniket Singh
1 Year agoGrade
Answers icon

1 Answer

Profile image of Askiitians Tutor Team
1 Year ago

Let's define the sides of the rectangle as follows:

Let the shorter side be denoted as a.
Let the longer side be denoted as b.
In a rectangle, the diagonal can be found using the Pythagorean theorem: Diagonal = √(a² + b²).

The problem states that the difference between the sum of adjacent sides and the diagonal is half the length of the longer side. This can be written as:

(a + b) - √(a² + b²) = b / 2.

Now, let's solve this step by step:

Step 1: Rearranging the equation to isolate the square root term: (a + b) - b / 2 = √(a² + b²).

Step 2: Simplifying the left-hand side: (a + b) - b / 2 = a + b/2.

Now we have: a + b/2 = √(a² + b²).

Step 3: Squaring both sides to eliminate the square root: (a + b/2)² = a² + b².

Step 4: Expanding the left-hand side: a² + 2a(b/2) + (b/2)² = a² + b². a² + ab + b²/4 = a² + b².

Step 5: Canceling out the common terms (a² and b²): ab + b²/4 = b².

Step 6: Subtracting b² from both sides: ab + b²/4 - b² = 0. ab - 3b²/4 = 0.

Step 7: Factoring out b: b(a - 3b/4) = 0.

Step 8: Since b ≠ 0, we can divide both sides by b: a - 3b/4 = 0.

Step 9: Solving for a: a = 3b/4.

Step 10: Now, we can find the ratio of the shorter side (a) to the longer side (b): a / b = (3b / 4) / b = 3/4.

Thus, the ratio of the shorter side to the longer side is 3:4.

The correct answer is D. 3:4.


question mark

Step 1: Building Number Understanding

Before children start solving sums, they must first understand numbers clearly.

Young learners should become familiar with:

  • Counting numbers

  • Recognising numbers

  • Understanding the value of numbers

Teachers often use simple activities such as counting objects, toys, or fruits to help children understand numbers.

For example, parents can ask questions like:

  • How many apples are on the table?

  • Can you count the pencils in your bag?

These small activities help children connect numbers with real objects.

Step 2: Learning Addition (Basic Sums)

Addition is usually the first mathematical operation children learn.

Addition means combining numbers together.

For example:

2 + 3 = 5

Teachers often teach addition using objects.

Example:

If a child has 2 pencils and receives 3 more pencils, the total becomes 5 pencils.

Using objects makes the concept easier to understand.

Simple addition practice

Parents can practice with children using:

  • fingers

  • small toys

  • beads

  • fruits

Once children understand the concept, they can move on to written sums.

Step 3: Understanding Subtraction

Subtraction means taking away from a number.

Example:

5 − 2 = 3

Teachers often explain subtraction using real situations.

Example:

If a child has 5 chocolates and gives 2 chocolates to a friend, how many chocolates remain?

This approach helps children understand subtraction more clearly.

Parents can encourage children to think about subtraction in everyday situations.

Step 4: Learning Multiplication

Multiplication is often introduced after children become comfortable with addition.

Multiplication means repeated addition.

Example:

3 × 4 means adding 4 three times.

4 + 4 + 4 = 12

Teachers often explain multiplication using groups.

Example:

If there are 3 groups of 4 apples, the total number of apples is 12.

Using pictures or objects helps children visualise multiplication easily.

Step 5: Multiplication Tables (Learning Vaaipaadu)

In Tamil education systems, multiplication tables are often called “vaaipaadu”.

Memorising tables helps children solve multiplication problems faster.

Common tables include:

2 × 1 = 2
2 × 2 = 4
2 × 3 = 6

Tables usually begin from 2 and go up to 10 or 12.

Teachers often encourage children to practice tables through:

  • repetition

  • rhythm or songs

  • daily practice

Parents can make table learning interesting by asking questions during daily activities.

For example:

If one box contains 5 chocolates, how many chocolates are there in 3 boxes?

These small questions strengthen table knowledge.

Step 6: Understanding Division

Division is the opposite of multiplication. It means sharing or splitting numbers equally.

Example:

12 ÷ 3 = 4

Teachers explain division using sharing examples.

Example:

If 12 sweets are shared equally among 3 children, each child receives 4 sweets.

This helps children understand the concept of division clearly.

Making Basic Maths Skills Practice Fun at Home

Mathematics should not feel like a stressful subject for children. Parents can help children enjoy maths through simple activities.

Some useful methods include:

Asking children to count objects around the house

Practicing tables during daily routines

Solving small sums during shopping or cooking

Playing number-based games

When maths becomes part of daily life, children learn faster.

Encouraging Confidence in Maths

Some children feel nervous about mathematics because they fear making mistakes.

Teachers usually encourage students to see mistakes as part of learning.

Parents can support children by:

  • appreciating their effort

  • encouraging them to try again

  • avoiding comparison with other students

Confidence grows when children feel supported.

Balancing Practice and Understanding

Memorising formulas or tables alone is not enough. Children should also understand the logic behind the calculations.

For example, a child who understands multiplication as repeated addition will find division easier to learn.

Teachers often recommend a balanced approach:

  • understanding concepts

     

  • regular practice

     

  • problem-solving exercises

This combination helps children build strong mathematical skills.

In our website Visit: https://jawaharglobalacademy.com/

Grade 1212 grade maths others

Last Activity: 1 Month ago