Question

One side of a rectangle is 4cm longer than the other. The perimeter of the rectangle is 28cm. Find the length of each side.

Please help, appreciate your helpfulness.

Answer 1

➤ Answer

• Length of rectangle = 9cm and breadth of rectangle = 5 cm.

➤ Given

• One side of a rectangle is 4 cm longer than the other.
• Perimeter of the rectangle = 28cm.

➤ To Find

• Length and breadth of the rectangle.

➤ Step By Step Explanation

➠ Assumption

Let us consider the breadth be x cm. then the length will be x + 4 cm.

➠ Formula Used

$\bigstar\underline{\boxed{\tt{\pink{Perimeter_{(Rectangle)} = 2(Length + Breadth)}}}}$

➠ By substituting the values

Let's substitute the value of length and breadth in the above formula.

$\longmapsto\tt 28 = 2(x + 4 + x) \\ \\\longmapsto\tt 28 = 2(2x + 4) \\ \\ \longmapsto\tt 28 = 4x + 8 \\ \\ \longmapsto\tt 28 - 8 = 4x \\ \\\longmapsto\tt 20 = 4x \\ \\\longmapsto\tt \cfrac{ \cancel{20}}{ \cancel4} = x \\ \\\longmapsto\bf{\green{ 5 \: cm = x}}$

➵ Therefore, length of rectangle = 4 + x => 9 cm and breadth of rectangle = 5 cm.

__________________________

Answer 2

The dimensions of the rectangle are as follows:

• Length = 9 cm
• Breadth = 5 cm

Step-by-step explanation

In the question, it has been stated that a side of a rectangle whose perimeter equals 28 cm is 4 cm longer than the other. We've been asked to determine the dimensions of the rectangle.

In order to find its length and breadth, first, we need to be clear with the expressions of them. On analysing, it can stated that its length equals (4 + b) units, while its breadth equals "b" units.

Since the its perimeter is equal to 28 cm, we can find their measurements by using the formula:

Breadth of the rectangle:

$\twoheadrightarrow \quad{ \sf{P = 2(l + b)}}$

Plugging in the values.

$\twoheadrightarrow \quad{ \sf{28 = 2(4 + b + b)}}$

Multiplying the expression inside the bracket with 2 in the RHS.

$\twoheadrightarrow \quad{ \sf{28 = 8 + 2b + 2b}}$

Adding the like terms 2b and 2b in the RHS.

$\twoheadrightarrow \quad{ \sf{28 = 8 + 4b}}$

Transposing the like terms from RHS to LHS. The number 8 will be transposed to the LHS. [In the LHS, it will be written as (– 8) since, it is added in the RHS.

$\twoheadrightarrow \quad{ \sf{28 - 8 = 4b}}$

Subtracting the numericals in the LHS.

$\twoheadrightarrow \quad{ \sf{20 = 4b}}$

Again transposing the like terms. This time, 4 will be transposed to the RHS. [The number 4 will be written with division symbol in the LHS, since it multiplied in the RHS]

$\twoheadrightarrow \quad{ \sf{20 \div 4= b}}$

Expressing the LHS in fractional form.

$\twoheadrightarrow \quad{ \sf{ \dfrac{20}{4} = b}}$

Reducing the fraction to its lowest form.

$\twoheadrightarrow \quad{ \sf{ \dfrac{5}{1} = b}}$

5/1 can also be written as follows.

$\twoheadrightarrow \quad{ \sf{5= b}}$

∴ The breadth of the rectangle is 5 cm.

Now, let us calculate the measure of its length by adding 4 to the measure of the breadth.

Length of the rectangle:

$\twoheadrightarrow \quad{ \sf{l = 4 + b}}$

Plugging in the values.

$\twoheadrightarrow \quad{ \sf{l = 4 + 5}}$

Adding the numericals.

$\twoheadrightarrow \quad{ \sf{l = 9}}$

∴ The length of the rectangle is 9 cm.