Question

If the length is 5 cm more than the breadth of a rectangle and perimeter is 130cm.Find the length and breadth of the rectangle



please give solution ​

Answer 1

ANSWER :

• ❖ If the length is 5 cm more than the breadth of a rectangle and perimeter is 130 cm; then Length of the rectangle is 35 cm and Breadth of the rectangle is 30 cm.

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SOLUTION :

❒ Given :-

• Length of the rectangle is 4 cm more than the Breadth of the rectangle.

• Perimeter of the rectangle = 130 cm

❒ To Find :-

• Length of the rectangle = ?

• Breadth of the rectangle = ?

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❒ Method 1 :-

Suppose,

• Length of the rectangle = l

• Breadth of the rectangle = b

Given that,

• Length is 5 cm more than breadth

Thus,

• l = b + 5 ———————> (1)

Again,

• Perimeter of the rectangle = 130 cm

We know that,

• $\dag \: \:\underline{ \boxed{ \sf{Perimeter \: \: of \: \: a \: \: rectangle = 2(Length + Breadth)}}}$

Using this formula we get,

• ✪ Perimeter of the rectangle = 2 ( l + b )

➜ 130 = 2 ( l + b )

➜ l + b = $\sf{\dfrac{130}{2}}$

∴ l + b = 65 ———————> (2)

Substituting the value of "l" from Eq. (1) in Eq. (2) we get,

• ★ ( b + 5 ) + b = 65

➜ b + 5 + b = 65

➜ 2b + 5 = 65

➜ 2b = 65 - 5

➜ 2b = 60

➜ b = $\sf{\dfrac{60}{2}}$

∴ b = 30

Substituting the value of "b" in Eq. (1) we get,

• ★ l = 30 + 5

∴ l = 35

Hence,

• Length of the rectangle, l = 35 cm

• Breadth of the rectangle, b = 30 cm

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❒ Method 2 :-

It is given that,

• Length of the rectangle is 5 cm more than breadth.

Suppose,

• Breadth of the rectangle, b = x

Then,

• Length of the rectangle will be, l = x + 5

Again,

• Perimeter of the rectangle = 130 cm

We know that,

• $\dag \: \:\underline{ \boxed{ \sf{Perimeter \: \: of \: \: a \: \: rectangle = 2(Length + Breadth)}}}$

Using this formula we get,

• ★ Perimeter of the rectangle = 2 ( l + b )

➜ 130 = 2 {(x + 5) + x}

➜ 130 = 2 (x + 5 + x)

➜ 130 = 2 (2x + 5)

Solving this equation, we get,

• ✪ 2x + 5 = $\sf{\dfrac{130}{2}}$

➜ 2x + 5 = 65

➜ 2x = 65 - 5

➜ 2x = 60

➜ x = $\sf{\dfrac{60}{2}}$

∴ x = 30

Substituting the value of "x" in (x + 5), we get,

• ✪ x + 5 = 30 + 5 = 35

Hence,

• Length of the rectangle, l = 35 cm

• Breadth of the rectangle, b = 30 cm