Question

A rectangular plot of land has length and breadth in the ratio 3:2. If the perimeter of the plot is 500 m, the length of the plot is *

150 m

100 m

200 m

180 m

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Answer 1

Solution

Given That :-

• A rectangular plot of land has length and breadth in the ratio 3:2.
• If the perimeter of the plot is 500 m

Find :-

• length of the plot .

Step - by - step -Explanation

Let,

• Length be = x
• Breadth be = y

Using Formula,

★ Perimeter of rectangle = 2 × [Length + Breath]

A/C to question,

(A rectangular plot of land has length and breadth in the ratio 3:2)

➡ x:y = 3:2

➡x/y = 3/2

➡2x - 3y = 0 _______(1)

Again

(The perimeter of the plot is 500 m)

➡perimeter of rectangular land = 2 × [ x + y]

➡ 500 = 2 × [x + y ]

➡2x + 2y = 500

➡2x + 2y = 500 __________(2)

Subtract equ(1) & equ(2)

➡ -3y - 2y = -500

➡ -5y = -500

➡ y = -500/(-5)

➡y = 100

Keep value of y in equ(1),

➡ 2x - 3*100 = 0

➡2x = 300

➡x = 300/2

➡x = 150

Hence

• Length be (x) = 150 m
• Length be (x) = 150 mBreadth be (y) = 100 m

__________________

Answer 2

Solution :

$\underline{\bf{Given\::}}}$

A rectangular plot of land has length & breadth in the ratio 3:2. If the perimeter of the Plot is 500 m.

$\underline{\bf{Explanation\::}}}$

Let the ratio of land has length & breadth be r respectively;

• Length = 3r
• Breadth = 2r

As we know that formula of the perimeter of rectangle;

$\boxed{\bf{Perimeter = 2(length + breadth)}}}$

A/q

$\longrightarrow\sf{2(3r + 2r ) = 500}\\\\\longrightarrow\sf{2(5r) = 500}\\\\\longrightarrow\sf{10r = 500}\\\\\longrightarrow\sf{r=\cancel{500/10}}\\\\\longrightarrow\bf{r=50\:m}$

Thus;

The length of the plot is 3r = 3 × 50m = 150 m .

Option (a)