Question

Of two squares, the sides of the larger are 5 cm longer than those of the smaller and

the area of the larger is 55 sq.cm more.What is the length of the sides of each ? ​

Answer 1

Answer:

325 cm

2

. The side of the larger square is 5 cm longer than the side of the smaller square. Find the side of each square.

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ANSWER

Let the side of square (1) = s

1

The side of 2

nd

square = a

Acc to Ques :

s=5+a _ (1)

and s

2

+a

2

=325 _ (2)

so, (5+a)

2

+a

2

=325

25+a

2

+10a+a

2

=325

2a

2

+10a=300

2a

2

+10a−300=0

a

2

+15a−5a−150=0

(a+15)(a−5)=0

∴a=5

and s=10

∴ side of smaller square = 5 cm

side of larger square = 10 cm

Answer 2

Answer :-

Taking the length of a side of the larger square as x centimeters and that of the smaller as y centimeters, we can write the fact's given as two equations :-

x - y = 5

$\bf \: x {}^{2} - y {}^{2} = 55$

Next,

Recall that ⤵️

$\bf \: x {}^{2} - y {}^{2} = (x + y)(x + y) \: this \: we \: can \: write \: as...$

$\bf \: x + y = \frac{x { }^{2 } - y {}^{2} }{x - y}$

So, in problem,

$\bf \: x + y = \frac{55}{5} = 11$

Now we have the sum x+y=11 and the difference, x - y = 5 . We can calculate the numbers as :

$\bf \: x = \frac{1}{2} (11 + 5) = 8$

$\bf \: y = \frac{1}{2} (11 - 5) = 3$

Thus the lengths of the sides of the square's are 8 centimeters and 3 centimeters