Question

The length of a rectangular plot is 40 more than the breadth and the perimeter of the plot is 92 m, find the dimensions of the plot. ​

Answer 1

Correct Question:-

The length of a rectangular plot is 40 more than the breadth and the perimeter of the plot is 92 m, find the dimensions of the plot.

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Answer:-

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Given:

▪︎Length of rectangular plot = breadth + 40

▪︎Perimeter of rectangular plot = 92m

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To Find:

▪︎Dimension of plot

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Solution:

According to given condition;

${\bf{Perimeter\ of\ rectangular\ plot = 92m}}$

${\bf{\implies 2(length+breadth) = 92m}}$

${\bf{\implies2(breadth + 40 + breadth) = 92}}$

${\bf{\implies breadth + breadth + 40 = 92 ÷ 2}}$

${\bf{\implies 2breadth = 46 - 40}}$

${\bf {\implies breadth = 6 ÷ 2}}$

${\bf{\therefore breadth = 3 m}}$

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Breadth = 3m

Length = 3 + 40 = 43m

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$\blue{\bf{Hence, Dimension\ of\ plot\ is\ 43m\ by\ 3m.}}$

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Formula to be remembered:-

▪︎Perimeter of square = 4 × Side

▪︎Area of square = Side²

▪︎Perimeter of square = 2(length + breadth)

▪︎Area of square = length × breadth

Answer 2

$\huge\bold{Solution :}$

${\sf\underline{\orange{Given :}}}$

The length of a rectangular plot is 40 more than the breadth and the perimeter of the plot is 92 m.

${\sf\underline{\green{To~Find :}}}$

The dimensions of the plot.

${\sf\underline{\blue{Solution :}}}$

Analysis :

Here the formula of perimeter of reactangle is used. Here we can see that the length and the breadth is dependent of each other. So we have to form equation. Using the perimeter of the reactangle We can solve the equation and get the dimensions.

Formula Required :

Perimeter of reactangle = 2(l + b)

Where,

• I is length
• B is breath

Explanation :

Let us assume that the breadth is "b" m and length is "b + 40" m.

• Perimeter = 92 m

We know that if we are provided with the perimeter of the reactangle and length and breadth are given in the form of equation then our required formula is,

Perimeter of reactangle is = 2(l + b)

Where,

• I = b + 40 m
• b = b m
• Perimeter is = 92 m

Using the required formula and Substituting the required values,

✬ According to the question,

➙ Perimeter of reactangle = 2(l + b)

➙ 92 = 2(b + 40 + b)

➙ 92 = 2(2b + 40)

➙ 92 = 4b + 80

➙ 92 - 80 = 40b

➙ 12 = 4b

➙ 12/4 = b

➙ 3 = b

.•. b = 3.

The dimensions are :

• Length = b + 40 = 3 + 40 = 43m
• Breathe = b = 3m

The dimensions of the plot are 43 m and 3 m.

Verification :

Perimeter of reactangle = 2(l + b)

Where,

• I = 43 m
• b = 3 m
• Perimeter = 92 m

Using the required formula and Substituting the required values,

✬ According to the question,

➙ Perimeter of the reactangle = 2(l + b)

➙ 92 = 2(43 + 3)

➙ 92 = 2(46)

➙ 92 = 2 × 46

➙ 92 = 92

.•. LHS = RHS.

• Hence verified.

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Hope it's helpful :)