Question

the difference of perimetres of 2 squares is 32 m and the difference there area is 208m what is the difference between lengtb of there sides​

Answer 1

difference of their Length = 8m

Step-by-step explanation:

Given :-

• The difference of perimetres of two squares is 32 m .
• The difference of their area is 208 m .

To find :-

• The difference between length of their sides .

Formula used :-

• Perimeter of square = 4 × side
• Area of square = side × side

Solution :-

Let x is the side of first square and y is side of another square .

So,

Perimeter of first square = 4x

Perimeter of another square = 4y

Difference of their perimeter = 32 m

4x – 4y = 32

divided by 4

x – y = 8 ............eq.(1)

Area of first square = x × x = x²

Area of another square = y × y = y²

Difference of their areas = 208 m²

x² – y² = 208

( x + y )( x – y ) = 208

( x + y ) × 8 = 208

x + y = 208/8

x + y = 26 ...........eq.(2)

add eq.(1) and eq.(2)

x – y = 8

x + y = 26

—————

2x = 34

x = 34/2

x = 17

Put the value of x = 17 in eq.(2)

x + y = 26

17 + y = 26

y = 26 – 17

y = 9

So, Length of first square = 17 m

and Length of another square = 9 m

Therefore, Difference of the Length

= ( 17 – 9 ) m

= 8 m

Hence, difference of their Length = 8m

We can also find the difference of Lenghts only with perimeter as difference of perimetres = 32

So,

4x – 4y = 32

divided by 4

x – y = 8

Here, also we have diffence of the Lengths.