Question

11. The area of a plot of land is 126 square metres. If the breadth
of the plot is 5 metres less than its Icngth, what will be be its length and
breedth 2​

Answer 1

☯ Length = 14 m & breadth = 9m

Given ,

• Area = 126m²
• Breadth = Length - 5

We need to find ,

• Length and breadth = ?

First finding length ,

=> Area = length × breadth

=> 126 = ( l - 5 ) × l

=> 126 = l² - 5l

=> l² - 5l - 126 = 0

We got a quadratic equation,

⇒ l² + 9l - 14l - 126 = 0

⇒ l ( l + 9 ) - 14 ( l + 9 ) = 0

⇒ ( l + 9 ) ( l - 14 ) = 0

⇒ l + 9 = 0 , l = - 9

⇒l - 14 = 0 , l = 14

⇒ l = -9 or 14

Since , length cannot be negative , we take 14

Now , breadth = length - 5 => 14 - 5 = 9 m

Hence ,

• Length = 14 m
• Breadth = 9 m

Answer 2

Question and answer -

Let's understand the concept 1st -

✰ This question says that the area of a plot of land is 126 m². The breadth of the plot is 5 metres less than the length of the plot. We have to find the length and breadth of the plot. It's cleared that plot is in the shape of a rectangle.

Given that -

✠ Area of a plot of land is 126 m².

✠ The breadth of the plot is 5 metres less than the length of the plot. ( B = l - 5 )

To find -

✠ Length of the plot.

✠ Breadth of the plot.

Solution -

✠ Length of the plot = 14 m

✠ Breadth of the plot = 9 m

Using concept -

✠ Formula to find area of rectangle.

Using formula -

✠ Area of rectangle = Length × Breadth

Full solution -

~ Let us find the length of the plot first,

⇢ Area of rectangle = Length × Breadth

⇢ Area of rectangular plot = Length × Breadth

According to the question,

⇢ 126 = l × (l-5)

⇢ 126 = l² - 5l

⇢ l² - 5l - 126 = 0 ( Quadratic equation )

Now,

⇢ l² + 9l - 14l - 126 = 0

⇢ l(l+9) - 14(l+9) = 0

⇢ (l+9) (l-14) = 0

⇢ (l-9) (l+14) = 0

⇢ l = -9 or 14

We can't take length into negative so,

⇢ l = 9 or 14

So,

★ Length = 14 metres

★ Breadth

= l - 5

= 14 - 5

= 9 metres

Additional information -

$\; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: cube \: = \: 6(side)^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto LSA \: of \: cube \:= \: 4(side)^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cube \: = \: (side)^{3}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diagonal \: of \: cube \: = \: \sqrt(l^{2} + b^{2} + h^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: cube \: = \: 4(l+b+h)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diameter \: of \: circle \: = \: 2r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cylinder \: = \: \pi r^{2}h}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Surface \: area \: of \: cylinder \: = \: 2 \pi rh + 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Lateral \: area \: of \: cylinder \: = \: 2 \pi rh}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Base \: area \: of \: cylinder \: = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Height \: of \: cylinder \: = \: \dfrac{v}{\pi r^{2}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: cylinder \: = \:\sqrt frac{v}{\pi h}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: rectangle \: = \:2(length+breadth)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: square \: = \: Side \times Side}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: triangle \: = \: \dfrac{1}{2} \times breadth \times height}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: paralloelogram \: = \: Breadth \times Height}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: circle \: = \: \pi b^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: triangle \: = \: (1st \: + \: 2nd \: + 3rd) \: side}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: paralloelogram \: = \: 2(a+b)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: cuboid \: = \: 2(l \times b + b \times h + l \times h}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto LSA \: of \: cuboid \: = \: 2h(l+b)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cuboid \: = \: L \times B \times H}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diagonal \: of \: cuboid \: = \: \sqrt 3l}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: cuboid \: = \: 12 \times Sides}}}$