Question

Q8 The side of one square is 3 cm longer than the side of the second square. The difference in their areas is 99 sq cm. Find the sides of the two squares.

Answer 1

Given :

• The side of one square is 3 cm longer than the side of the second square.
• The difference in their areas is 99 cm².

To find :

• Sides of two squares.

Solution :

Let the side of 1st square be x cm and the side of 2nd square be y cm.

According to 1st condition :-

• The side of one square is 3 cm longer than the side of the second square.

$\implies\sf{x=y+3...........eq(1)}$

We know,

${\boxed{\bold{\large{Area\: of\: square=side^2}}}}$

★ Area of 1st square= x² cm²

★ Area of 2nd square =y² cm²

According to 2nd condition :-

• The difference in their areas is 99 cm².

$\implies\sf{x^2-y^2=99}$

✪ Put x = y+3 from eq(1) ✪

$\implies\sf{(y+3)^2-y^2=99}$

$\implies\sf{y^2+6y+9-y^2=99}$

$\implies\sf{6y+9=99}$

$\implies\sf{6y=99-9}$

$\implies\sf{6y=90}$

$\implies\sf{y=15}$

${\boxed{\bold{y=15}}}$

Put y = 15 in eq(1) for getting the value of x.

$\implies\sf{x=y+3}$

$\implies\sf{x=15+3}$

$\implies\sf{x=18}$

${\boxed{\bold{x=18}}}$

Therefore,

The side of 1st square is 18 cm and the side of 2nd square is 15 cm.

Answer 2

$\huge{\underline{\underline{\mathrm{\red{GIVEN:-}}}}}$

• The side of one square is 3 cm longer than the side of the second square
• The difference in their areas is 99 sq cm

$\huge{\underline{\underline{\mathrm{\red{NEED\:TO\:FIND:-}}}}}$

Find the sides of the two squares = ?

$\huge{\underline{\underline{\mathrm{\red{FORMULA\:USED:-}}}}}$

$\large{\boxed{\bf{\blue{Area\:of\:square = {(side)}^{2}}}}}$

$\huge{\underline{\underline{\mathrm{\red{SOLUTION:-}}}}}$

Let the sides of one square be 'x' cm

and,

the sides of another square be 'y' cm

According to Question :-

If the side of one square is 3 cm longer than the side of the another square

$\implies$$\large\bf\blue{<strong> </strong><strong> </strong>x = y + 3.....(1)}$

We know that, the formula to calculate the area of square :- (side)²

If the difference in their areas is 99 cm²,

$\implies$$\large\bf\blue{{x}^{2} - {y}^{2} = 99 ......2)}$

Put the value of x from equation ....1)

$\implies$$\bf{{y + 3}^{2} - {y}^{2} = 99}$

$\implies$$\bf{{y}^{2} + 2\times y\times 3 + {3}^{2} - {y}^{2} = 99}$......[ Using identity ( a + b)² = a² + 2ab + b² ]

$\implies$$\bf{6y + 9 = 99}$

$\implies$$\bf{6y = 99-9}$

$\implies$$\bf{6y = 90}$

$\implies$$\bf{y = }$$\cancel\dfrac{90}{6}$

$\large{\boxed{\bf{\green{y = 15}}}}$

Put the value of y in equation .....1)

$\implies$$\large\bf{x = y + 3}$

$\implies$$\bf{x = 15 + 3}$

$\large{\boxed{\bf{\green{x = 18}}}}$

Thus, the side of one square is 18 & the side of another square is 15

$\large{\underline{\underline{\mathrm{\red{FINAL\: ANSWER:-}}}}}$

$\huge{\boxed{\boxed{\bf{\green{x = 18}}}}}$

$\huge{\boxed{\boxed{\bf{\green{y = 15}}}}}$

$\huge{\underline{\underline{\mathrm{\red{VERIFICATION:-}}}}}$

Putting the value of x and y in equation 1)

$\implies$$\large\bf{x = y + 3}$

$\implies$$\bf{18= 15 + 3}$

$\implies$$\bf{18= 18 }$

Putting the value of x and y in equation 2)

$\implies$$\large\bf{{x}^{2} - {y}^{2} = 99 }$

$\implies$$\large\bf{{18}^{2} - {15}^{2} = 99 }$

$\implies$$\large\bf{324 - 225 = 99 }$

$\implies$$\large\bf{99 = 99 }$

$\huge\rm\underline\red{VERIFIED}$