Question

the perimeter of two squares differ by 4.0 cm. The sum of the perimeters for the two squares is 16.0 cm. What is the side length of the larger sqaure

Answer 1

Answer:

2.5 cm

Step-by-step explanation:

Given :

• The perimeter of two squares differ by 4.0 cm.
• The sum of the perimeters for the two squares is 16.0 cm

To find :

the length of the side of the larger square

Solution :

Let 'A' cm be the side length of the larger square and 'a' cm be the side length of the smaller square.

We know,

Perimeter of a square = 4 × side

Perimeter of larger square = 4A

Perimeter of smaller square = 4a

They differ by 4 cm.

Perimeter of larger square – Perimeter of smaller square = 4 cm

4A – 4a = 4

4(A – a) = 4

A – a = 1 –[1]

Their sum is 16 cm

Perimeter of larger square + Perimeter of smaller square = 16 cm

4A + 4a = 16

4(A + a) = 4(4)

A + a = 4 –[2]

Add both the equations,

A – a + A + a = 1 + 4

2A = 5

A = 5/2

A = 2.5 cm

Therefore, the length of the side of the larger square is 2.5 cm

Answer 2

Step-by-step explanation:

$\underline{\underline{\maltese\: \: \textbf{\textsf{Question}}}}$

• The perimeter of two squares differ by 4.0cm. The sum of the perimeters for the two squares is 16.0cm. What is the side length of the larger sqaure ?

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

• The length of the side of the larger square is 2.5cm.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Given}}}}$

• The perimeter of two squares differ by 4.0cm.
• The sum of the perimeters for the two squares is 16.0cm.

$\underline{\underline{\maltese\: \: \textbf{\textsf{To\ Find}}}}$

• We have to find out the length of the side of the larger square.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Basic\ Terms}}}}$

• Perimeter : Perimeter is the distance around a two-dimensional shape.
• Square : In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles.
• Length : Length is the distance from one end to the other end of an object.
• Side : In geometry, side can be defined as the line segment that joins two vertices in a shape or two-dimensional figure.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Solution}}}}$

• As per the given information, we know that there are two squares whose perimeter differ by 4cm. And the sum of both the perimeter is 16cm.
• Then firstly, we will take 'A' cm as the side length of the larger square and 'a' cm as the side length of the smaller square.
• So, by using the required information given in the question we will create equations. And after that, by adding the equations we will get the length of the side of the larger square.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Calculations}}}}$

We know that :-

${\underline{\boxed{\sf {Perimeter\ of\ square\ =\ 4 \times side}}}}$

Here,

• Side = 'A' cm (Larger square) and,
• Side = 'a' cm (Smaller square).

By applying the values, we get :-

$\sf \mapsto {Perimeter\ of\ square\ =\ 4 \times side}$

$\sf \mapsto {Perimeter\ of\ larger\ square\ =\ 4 \times A}$

${\therefore{\underline{\boxed{\tt {Perimeter\ of\ larger\ square\ =\ 4A.}}}}}$

~And,

$\sf \mapsto {Perimeter\ of\ square\ =\ 4 \times side}$

$\sf \mapsto {Perimeter\ of\ smaller\ square\ =\ 4 \times a}$

${\therefore{\underline{\boxed{\tt {Perimeter\ of\ smaller\ square\ =\ 4a.}}}}}$

• As we know, that the perimeter of both the squares differ by 4cm.
• So, now we will create equation 1.
• So, by using a required formula we will create equation 1 by using required values.

Required formula is as follows :-

${\underline{\boxed{\sf {Perimeter\ of\ larger\ square\ -\ Perimeter\ of\ smaller\ square\ =\ 4cm}}}}$

Here,

• Perimeter of larger square = 4A.
• Perimeter of smaller square = 4a.

By applying the values, we get :-

$\sf \mapsto {Perimeter\ of\ larger\ square\ -\ Perimeter\ of\ smaller\ square\ =\ 4cm}$

$\sf \mapsto {4A\ -\ 4a\ =\ 4}$

$\sf \mapsto {4(A\ -\ a)\ =\ 4}$

~So, 1st equation is as follows :-

${\therefore{\underline{\boxed{\tt {A\ -\ a\ =\ 1.}}}}}$

• We also know, that the sum of perimeter of both the squares is 16cm.
• So, now we will create equation 2.
• So, by using a required formula we will create equation 2 by using the required values.

Required formula is as follows :-

${\underline{\boxed{\sf {Perimeter\ of\ larger\ square\ +\ Perimeter\ of\ smaller\ square\ =\ 16cm}}}}$

Here,

• Perimeter of larger square = 4A.
• Perimeter of smaller square = 4a.

By applying the values, we get :-

$\sf \mapsto {Perimeter\ of\ larger\ square\ +\ Perimeter\ of\ smaller\ square\ =\ 16cm}$

$\sf \mapsto {4A\ +\ 4a\ =\ 16}$

$\sf \mapsto {4(A\ +\ a)\ =\ 4(4)}$

~So, 2nd equation is as follows :-

${\therefore{\underline{\boxed{\tt {A\ +\ a\ =\ 4.}}}}}$

• Now, we have equation 1 and equation 2.
• So, by adding both the equations we will get the length of the side of the larger square.

$\sf \mapsto {A\ -\ a\ +\ A\ +\ a\ =\ 1\ +\ 4}$

$\sf \mapsto {2A\ =\ 5}$

$\sf \mapsto {A\ =\ \cancel \dfrac{5}{2}}$

$\sf \mapsto {A\ =\ 2.5cm}$

${\therefore{\underline{\boxed{\tt {Length\ of\ side\ of\ the\ larger\ square\ =\ 2.5cm.}}}}}$