Question

Find the area of a rectangle. the perimeter is 92m the lenght is 6 more than 4 times the width

Answer 1

Gɪᴠᴇɴ :-

• Perimeter of Rectangle = 92m.
• the Length is 6 more than 4 times the width.

Tᴏ Fɪɴᴅ :-

• Area of Rectangle ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• Perimeter of Rectangle = 2(Length + Breadth).
• Area of Rectangle = Length * Breadth .

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That , Breadth of Rectangle is x m.

So,

→ Length = 6 more than 4 times the Breadth .

→ Length = 6 + 4*x

→ Length = (4x + 6)m.

Therefore,

→ Perimeter of Rectangle = 2(Length + Breadth).

→ 2(4x + 6 + x) = 92

→ 5x + 6 = 46

→ 5x = 46 - 6

→ 5x = 40

→ x = 8m.

Hence,

→ Breadth of Rectangle = 8m.

→ Length of Rectangle = 8*4 + 6 = 32 + 6 = 38m.

So,

→ Area of Rectangle = Length * Breadth .

→ Area of Rectangle = 38 * 8

→ Area of Rectangle = 304m². (Ans.)

Hence, Area of Rectangle will be 304m².

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

◕ Let the breadth of the rectangle be x

${\implies{\sf{\green{length \: of \: the \: rectngle \: is \: 6 \: more \: than \: the \: width}}}}$

◕Length of rectangle be = 6+4x

$\star{\sf{\orange{perimeter \: of \: rectangle = 2(length + breadth}}}$

${\implies{\bf{2(4x + x + x ) = 96}}}$

${\implies{\bf{10x + 8 = 92}}}$

${\implies{\bf{10x= 92 - 12}}}$

${\implies{\bf{10x=80}}}$

${\implies{\bf{x= \frac{80}{8} }}}$

${\implies{\bf{x=8}}}$

$\star{\sf{\underline{\blue{area \: of \: rectangle = length \times breadth}}}}$

${\implies{\bf{38 \times 8}}}$

${\implies{\bf{304 {m}^{2} }}}$