Question

Find the dimensions of a rectangle whose perimeter is 28m and area is 40 sq.m​

Answer 1

$\Huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

$\Large{\sf{Given :}}$

Area of rectangle is 40 sq. m

Perimeter of rectangle is 28 m.

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$\LARGE{\sf{To \: Find :}}$

Length and breadth of rectangle

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$\LARGE{\sf{Solution :}}$

We know that,

$\LARGE{\boxed{\boxed{\green{\tt{Area = L \times B}}}}}$

(Putting values)

40 = L × B......... (1)

$\LARGE{\boxed{\boxed{\green{\tt{Perimeter = 2( L + B)}}}}}$

(Putting values)

28 = 2(L + B)

→ 28/2 = L + B

→ 14 = L + B......... (2)

From equation 2.

→ 14 - L = B

Put the value of B in equation 1.

→ 40 = (14 - L)(L)

→ 40 = 14 L - L²

→ -L² + 14L - 40 = 0

→ -(L² - 14L + 40) = 0

→ L² - 10L - 4L + 40 = 0

→ L (L - 10) -4 (L - 10) = 0

→ (L 10)(L - 4) = 0

So, L can be 10 or 4.

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When Length 10 put value in equation 2.

14 = 10 + B

→ 14 - 10 = B

→ 4 = B

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Now,

When length is 4 then put value in equation 2.

14 = 4 + B

→ 14 - 4 = B

→ 10 = B

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We know that,

Breadth is always shorter than the length.

So Length is 10m and Breadth is 4m.

$\Large{\boxed{\red{\sf{Length \: = \: 10 \: m}}}}$

$\Large{\boxed{\red{\sf{Breadth \: = \: 4 \: m}}}}$

Answer 2

ANSWER:-

Given:

The perimeter of rectangle is 28m & the area is 40m².

To find:

The dimensions of a rectangle.

Explanation:

We know that perimeter of rectangle: 2(Length + Breadth)

Area of rectangle: Length × Breadth sq. unit

According to the question:

• Perimeter of rectangle;

⇒ 2(length+ breadth)=28

⇒ length + breadth= $\frac{28}{2}$

⇒ length+ breadth= 14m......................(1)

&

• Area of rectangle:

⇒ Length × Breadth= 40

⇒ Breadth= $\frac{40}{Length}$......................(2)

Putting the value of breadth in equation (1), we get;

= $l + \frac{40}{l} =14$

$= l^{2} +40=14l\\\\=l^{2} -14l+40=0\\\\= l^{2} -4l-10l+40=0\\\\=l(l-4)-10(l-4)=0\\\\=(l-4)(l-10)=0\\\\=l-4=0\:\: or \:\: l-10=0\\\\=l=4\:\:or\:\:l=10$

Therefore,

From equation (1), putting l=4 we get;

⇒ 4 + b= 14

⇒ b= 14 -4

⇒ b= 10.

&

Again,

Putting the value of l= 10, in equation (1), we get;

⇒ 10+ b= 14

⇒ b= 14- 10

⇒ b= 4.

Thus,

• Breadth= 4m
• Length= 10m

The dimensions of a rectangle is 10 & 4.