Question

the length and the breadth of a rectangle field are in the ratio 5:3 if its perimeter is 128,find the dimensions of the field ​

Answer 1

$\huge\sf{\underline{\underline{Answer}}}$

The Length is 40 m and Breadth is 24 m.

$\bold{Given:}$

• Ratio of Length to Breadth = 5 : 3

• Perimeter = 128 m

$\bold{To\: find:}$

• Dimensions of field

______________________________

Let the -

• Length be 5y

• Breadth be 3y

$\boxed{Perimeter = 2(Length + Breadth)}$

⇒ 128 = 2(5y + 3y)

⇒ 128 = 10y + 6y

⇒ 128 = 16y

⇒ y = $\frac{128}{16}$

⇒ y = 8

Length = 5 × 8 = 40 m

Breadth = 3 × 8 = 24 m

∴ The Length is 40 m and Breadth is 24 m.

#BAL

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Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\green{ANSWER\::}}}}}}$

$\bold{\Large{\underline{\sf{\pink{Given\::}}}}}$

The length and the breadth of a rectangle field are in the ratio 5:3, if its perimeter is 128m.

$\bold{\Large{\underline{\sf{\red{To\:find\::}}}}}$

The dimensions of the field.

$\bold{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

Let the ratio be R.

$\bold{We\:have}\begin{cases}\sf{The\:length\:of\:rectangular\:field=5R}\\ \sf{The\:breadth\:of\:rectangular\:field=3R}\\ \sf{Their\:perimeter=128m}\end{cases}$

We know that perimeter of rectangle: 2(length + breadth)

→ 2(5R + 3R) = 128

→ 2(8R) = 128

→ 16R = 128

→ R = $\bold{\cancel{\frac{128}{16} }}$

→ R = 8m.

Now,

• The dimensions of the field:

The length of rectangular field = 5(8)m = 40m.

The breadth of rectangular field = 3(8)m = 24m.