Question

A rectangle has the area equal to that of a square of side 80 cm. In the
aromat of a square of side 80 cm. If the breadth of the rectangle
is 20 cm, find its length.​

Answer 1

➽ Correct Question :- A rectangle has the area equal to that of a square of side 80 cm. If the breadth of the rectangle is 20 cm, fInd the length of rectangle.

Given:

• Measure of length of side of square is 80 cm.
• Measure of breadth of rectangle is 20 cm.
• Area of rectangle = Area of square.

To Find:

• What is the measure of length of rectangle ?

Solution: Let the length of rectangle be L cm and breadth is given 20 cm. Therefore

★ Area of Rectangle = ( Length x Breadth ) ★

$\implies{\rm }$ Area = ( L $\times$ 20 ) cm²

$\implies{\rm }$ Area = 20L cm²

So, the area of rectangle is 20L cm²...(1)

Now, As we know that :-

★ Area of Square = ( Side )² ★

• Side = 80 cm

$\implies{\rm }$ Area = ( 80 )² cm²

$\implies{\rm }$ Area = ( 80 $\times$ 80 ) cm²

$\implies{\rm }$ Area = 6400 cm²

So, the area of square is 6400 cm²....(2)

A/q

• Equation 1 = Equation 2

➟ 20L cm² = 6400 cm²

➟ L = 6400/20

➟ L = 320 cm

Hence, the measure of length of rectangle is 320 cm.

________________________

★ Verification ★

➫ Length x Breadth = Side²

➫ 320 x 20 = 80²

➫ 6400 = 6400

[ Verified ]

Answer 2

CORRECT QUESTION:

A rectangle has the area equal to that of a square of side 80 cm. If the breadth of the rectangle is 20 cm, find its length.

GIVEN:

• Side of the square = 80 cm
• Breadth of the rectangle = 20 cm
• Area of rectangle = Area of square

TO FIND:

• What is the length of the rectangle ?

FORMULA USED:

$\Large\bf{ L \times B = {(a)}^{2}}$

SOLUTION:

Let the length of the rectangle be 'x' cm

According to question:-

✫ Area of Rectangle = Area of square ✫

$\bf{ L \times B = {(a)}^{2}}$

On putting the given values in the formula, we get

$\rm{\longrightarrow x \times 20 = {(80)}^{2}}$

$\rm{\longrightarrow 20x = 6400}$

$\rm{\longrightarrow x = \cancel\dfrac{6400}{20}}$

$\bf{\longrightarrow \star \: x = 320 \: cm\: \star }$

⚫ Length = x = 320 cm

❝ Hence, the Length of the rectangle is 320 cm ❞

____________________

VERIFICATION:

Put the value of L and B in the formula

➾ $\rm{320 \times 20 = {(80)}^{2}}$

➾ $\bf{6400 = 6400}$

[L.H.S. = R.H.S.]

VERIFIED....