Question

pls answer it is urgent​

Answer 1

$\underline{\underline{\maltese\:\:\textbf{\textsf{Question}}}}$

• Shirish has a rectangular plot of land. When he measures it's dimensions, he finds that the Length is 20 m more than the Breadth. He decides to put a fence around it. He contacts few contractors. The lowest price quoted is ₹ 37.50 per meter. Shirish gets the job done by contractor and pays him ₹ 7500. What is the Length of plot ?

$\underline{\underline{\maltese\:\:\textbf{\textsf{Given}}}}$

• Shape of Shirish's Plot of Land is Rectangle
• Length of Rectangle = 20 m + x (Assuming Breadth = x)
• Breadth of Rectangle = x  (Assuming Breadth = x)
• The lowest price quoted for fencing the land = ₹ 37.50 per meter
• Amount Paid by Shirish for fencing the land = ₹ 7500
• To Find : Length of Plot

$\underline{\underline{\maltese\:\:\textbf{\textsf{Solution}}}}$

Since the Shape of Shirish's Plot of Land is Rectangle, Perimeter of Plot = Perimeter of Rectangle. We are all aware of formula to calculate Perimeter of Rectangle! It's Simple ; Perimeter of Rectangle = 2 × (Length + Breadth)

$\longrightarrow$ Perimeter of Plot = Perimeter of Rectangle

$\longrightarrow$ Perimeter of Plot = 2 × (Length + Breadth)

$\longrightarrow$ Perimeter of Plot = 2 × [(20 m + x) + (x)]

We need to get rid of Parentheses, So remove Parentheses! If there is a negative sign in front of it, each term within the expression changes sign. Otherwise, the expression remains unchanged

$\longrightarrow$ Perimeter of Plot = 2 × [20 m + x + x]

$\longrightarrow$ Perimeter of Plot = 2 × (20 m + 2x)

We need to expand this term by multiplying a term and an expression. For that, Apply Distributive Law Over Addition : a × (b + c) = ab + ac

$\longrightarrow$ Perimeter of Plot = 2 × (20 m) + 2 × (2x)

$\longrightarrow$ Perimeter of Plot = 40 m + 4x

Now, Multiply Perimeter of Plot with Cost of Fencing the Land per meter and equate it to Total Amount paid by Shirish for Fencing the Land! From This We can find the Breadth of the Rectangular Plot

$\longrightarrow$ (40 m + 4x) × ₹ 37.50 = ₹ 7500

Divide Both Sides of the Equation by 37.50

$\longrightarrow$ 40 m + 4x = ₹ 7500 ÷ ₹ 37.50

$\longrightarrow$ 40 m + 4x = 200

Subtract 40 m from Both Sides of the Equation!

$\longrightarrow$ 40 m + 4x - 40 m = 200 - 40 m

$\longrightarrow$ 4x = 160 m

Divide Both Sides of the Equation by 4

$\longrightarrow$ x = 160/4 m

$\longrightarrow$ x = 40 m       ------- (Breadth of the Rectangle)

Now We can find the Length of Rectangle from the Value of Breadth by adding 20 m to the Breadth!

$\longrightarrow$ Length of Rectangle = Breadth of Rectangle + 20 m

$\longrightarrow$ Length of Rectangle = 40 m + 20 m

$\longrightarrow$ Length of Rectangle = 60 m

Therefore, Length of Plot = 60 m