Question

1. Of two squares the sides of the larger are 4cm longer than those of the
smaller and the area of the larger is 72 sq.cm more than the smaller
Consider the sides of larger square as x and smaller as y. Then
a) What is the value of x-y?
b) Find x²-y²?
c) Calculate x+y?
d) What are the length of the sides of both square?​

Answer 1

Answer:

Applying the above condition, we get

x

2

+(x+4)

2

=656

2x

2

+8x+16=656

2x

2

+8x−640=0

x

2

+4x−320=0

(x+2)

2

=324

(x+2)

2

=18

2

Now length cannot be negative, hence

x+2=18

x=16 cm

Hence, (x+4)=20 cm.

hope this will help you

Answer 2

Let :

• Side of larger square = x
• Side of smaller square = y

Given:

• Side of larger square is 4cm more than side of smaller square
• Area of larger square is 72 cm² more than area of smaller square

To find :

a) x - y

b) x²-y²

c) x+y

d) Length of side of both square (x & y)

Formula used :

• Area of square = side²

Solution :

(a)

$\bullet \: \sf Side \: of \: larger \: square \: = \: 4cm \: + \: side \: of \: smaller \: square \: \\ \\ \: \sf \: \implies \: x \: = \: 4cm + y \\ \\ \sf \implies \: x - y \: = \: 4cm$

(b)

$\bullet \sf \: Area \: of \: larger \: square \: \: = 72 {cm}^{2} + area \: of \: smaller \: square \: \\ \\ \sf \implies \: {x}^{2} = 72 {cm}^{2} + {y}^{2} \\ \\ \sf \implies \: {x}^{2} - {y}^{2} = 72 {cm}^{2}$

(c)

We know that ,

• x² - y² = 72
• x - y = 4

using identity, (a+b)(a-b) = a² - b²

We get;

$\implies \sf \: {x}^{2} - {y}^{2} = (x + y)(x - y) \\ \\ \implies \sf \:72 = (x + y) \times 4 \\ \\ \implies \sf \:(x + y) \: = \: \dfrac{72}{4} \\ \\ \implies \sf \: \: (x + y) \: = \: 18$

(d)

From above, we have

• x + y = 18 ..... equation 1
• x - y = 4 ........ equation 2

On Adding equation 1 and 2 , we get;

$\implies \sf \: (x + y) \: + \: (x - y) \: = \: 18 \: + \: 4 \\ \\ \implies \sf \: 2x \: = \: 22 \\ \\ \implies \sf \: x \: = \: 22 \div 2 \\ \\ \implies \sf \: x \: = 11$

Now , on putting value of x in equation 1, we get;

$\implies \sf \: 11 \: + \: y \: = \: 18 \\ \\ \implies \sf \: y \: = \: 18 \: - \: 11 \\ \\ \implies \sf \: y \: = \: 7$

ANSWER :

(a) x - y = 4

(b) x² - y² = 72

(c) x + y = 18

(d) x = 11 and y = 7