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

Explanation:

let side of 1st square be x and side of second square be x+3

diff of areas= 99

(x+3)² - x² = 99

x² + 6x + 9 - x² = 99

6x + 9 = 99

6x = 90

x = 90/6

x = 15

side of 1st square = 15 cm

side of 2nd square = 18 cm

Verification

area of 1st square = 15² = 225 cm²

area of 2nd square = 18² = 324 cm²

diff between area = 324-225 = 99

therefore verified

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Answer 2

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

• The difference in their areas is = 99 cm²

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What are the sides of two squares?

Formula to be used :-

• Area of a square = a²

Where, a = side

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

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

As per question :-

Given that,

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

Therefore,

⟹ x = y + 3................. eq(1)

Again, it’s given that

The difference in their areas is 99 cm².

Hence,

• Area of 1st square is = x² cm²

• Area of 2nd square is =y² cm²

According to the question :-

x² - y² = 99............. eq(2)

Now, put x = y +3 in eq(2) for getting the value of y.

x² - y² = 99

⟹ (y +3)² - y² = 99

⟹ 6y +9 = 99

⟹ 6y = 90

⟹ y = 15

Substituting the value of y in eq (1), we get

x = y +3

⟹ x = 15 +3

⟹ x = 18

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