Question

If the area of rectangle is 60 cm. And perimeter is 38 cm then find its sides.​

Answer 1

Required Answer:-

Correct Question:

• If the area of a rectangle is 60cm² and it's perimeter is 38cm, find the length of its side.

Solution:

→ Let the length of the rectangle be x cm.

→ Let the breadth of the rectangle be y cm.

We know that,

→ Area of the rectangle = Length × Breadth.

So,

→ A = xy

Here,

→ A = 60 cm²

→ xy = 60cm²

→ y = 60/x — (i)

We know that,

→ Perimeter of a rectangle = 2 × (Length + Breadth)

→ P = 2(x + y)

Here,

→ P = 38cm

→ 2(x + y) = 38

→ x + y = 19 cm

Substituting the value of y here, we get,

→ x + 60/x = 19

→ (x² + 60)/x = 19

→ x² + 60 = 19x

→ x² - 19x + 60 = 0

Now, solve for x.

→ (-15) × (-4) = 60 and (-15) + (-4) = -19

→ x² - 15x - 4x + 60 = 0

→ x(x - 15) - 4(x - 15) = 0

→ (x - 4)(x - 15) = 0

By zero product rule,

→ Either (x - 4) = 0 or (x - 15) = 0

→ x = 4cm, 15cm

So, when x = 4cm

→ y = 60/4

→ y = 15

→ But x > y as x is the length.

→ x ≠ 4 cm

→ x = 15cm

So,

→ y = 60/15 cm

→ y = 4cm

Therefore,

→ Length of the rectangle = 15cm.

→ Breadth of the rectangle = 4cm.

Answer:

• Length of the rectangle = 15cm.
• Breadth of the rectangle = 4cm.

Answer 2

Answer :-

Given :-

• Area of rectangle = 60 cm²
• Perimeter = 38 cm

To Find :-

• Length and breadth

Solution :-

Let length be l and breadth be b

We know that,

Area of rectangle = Length × Breadth

⇒ l × b = 60

Also,

Perimeter = 2 ( Length + Breadth )

⇒ 38 = 2 ( l + b )

⇒ l + b = 38 / 2

⇒ l + b = 19

Now, we have two equations :-

⇒ l + b = 19 - i

⇒ l × b = 60 - ii

Solving the two equations and finding the value of l and b

Squaring equation i :-

⇒ (l + b)² = 19²

⇒ l² + b² + 2lb = 361

⇒ l² + b² + 2 ( 60 ) = 361

⇒ l² + b² + 120 = 361

⇒ l² + b² = 241

Now, calculating value of ( l - b )

⇒ (l - b)² = l² + b² - 2lb

⇒ (l - b)² = 241 - 2 ( 60 )

⇒ (l - b)² = 241 - 120

⇒ (l - b)² = 121

⇒ l - b = √121

⇒ l - b = 11

Now, we have -

⇒ l + b = 19 - i

⇒ l - b = 11 - iii

Adding equation i and iii :-

⇒ l + b + l - b = 19 + 11

⇒ 2l = 30

⇒ l = 15

Substituting the value in equation 1 :-

⇒ l + b = 19

⇒ 15 + b = 19

⇒ b = 4

Hence, length of rectangle = 15 cm Breadth of rectangle = 4 cm