Question

The length of a rectangular plot is 10 m more than the breadth and the length of its
fence is 22 m less than 5 times the breadth. Find the dimensions of the plot.​

Answer 1

Step-by-step explanation:

Given:-

The length of a rectangular plot is 10 m more than the breadth

and the length of its fence is 22 m less than 5 times the breadth.

To find:-

Find the dimensions of the plot.

Solution:-

Let the breadth of the rectangle be 'X' m

Then,

The the length of the rectangle=10 m more than breadth=(X+10) m

The perimeter of the rectangle=2(l+b) units

=>P=2(X+10+X)

=>P=2(2X+10)

=>P=(4X+20) m --------(1)

According to the given problem,

the length of its fence is 22 m less than 5 times the breadth.

=>P=(5X-22)m ------(2)

From (1)&(2)

=>4X+20=5X-22

=>20+22=5X-4X

=>44=X

=> X=44

X+10=44+10=55

Answer:-

Length of the rectangle=55m

Breadth of the rectangle=44m

Check:-

Length=breadth+10=44+10=55m

Length of the fence=22 m less than 5 times the breadth. =5(44)-22=220-22=198m

perimeter=2(55+44)=2(99)=198m

verified the given relations

Answer 2

Answer:

Step-by-step explanation:

Let the breadth of the rectangle be 'X' m

Then,

The the length of the rectangle=10 m more than breadth=(X+10) m

The perimeter of the rectangle=2(l+b) units

=>P=2(X+10+X)

=>P=2(2X+10)

=>P=(4X+20) m --------(1)

According to the given problem,

the length of its fence is 22 m less than 5 times the breadth.

=>P=(5X-22)m ------(2)

From (1)&(2)

=>4X+20=5X-22

=>20+22=5X-4X

=>42=X

=> X=42

X+10=42+10=52

Answer:-

Length of the rectangle=52m

Breadth of the rectangle=42m

Check:-

Length=breadth+10=42+10=52m

Length of the fence=22 m less than 5 times the breadth. =5(42)-22=210-22=188m

perimeter=2(52+42)=2(94)=188m

VERIFIED!