Question

the sum of the areas of two squares is 400 square metre if the difference between their perimeters is 16 find the side of the square the sum of the squares of the sum of the areas of two squares is 400 square metre if the difference between their perimeter is 16 find the side of the squares ​

Answer 1

Step-by-step explanation:

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

difference in perimeter of two squares:-

4x-4y=16

4(x-y)=16

x-y=16/4

therefore, x-y=4

and x=4+y---take this(1)

 

sum of areas of two squares:-

 x²+y²=400

Put (1) here

(4+y)²+y²=400

(4)²+(y)²+2×4×y+y²=400

16+y²+8y+y²=400

2y²+8y+16-400=0

2y²+8y-384=0

2(y²+4y-192)=0 (here we have taken 2 common and take to another side. then it becomes:-)

y²+4y-192=0

we have done with factorisation method:-

y²-12y+16y-192=0

y(y-12)+16(y-12)=0

(y+16) (y-12)=0

either:-                             |             or:-

y+16=0                            |                   y-12=0

y= -16                              |                   y=12

we will take y=12 because y being side cannot be negative.

So, y=12

put y=12 in (1)

x=4+y

x=4+12

therefore, x=16

and hence, Side of first square= x = 16

and Side of another square= y = 12.

AND DONE