Question

the length of a rectangle plot is 8m longer than its breadth.If the area of plot is 308msq,find the length and breadth if the plot​

Answer 1

Answer:

◔ Length of plot $\mapsto\:{\boxed{\tt{\red{22\:m}}}}$

◔ Breadth of plot $\mapsto\:{\boxed{\tt{\pink{14\:m}}}}$

Explanation:

Given information,

The length of a rectangle plot is 8 m longer than it's breadth. If the area of plot is 308 m². Find the length and breadth of the plot.

Let,

• Let breadth = x m
• So, length = (x + 8) m

Using formula,

◒ $\boxed{\underline{\underline{\bf{\purple{Area_{(rectangle)} = L\:\times\:B}}}}}\:\bf{\dag}$

Where,

• '$\sf Area_{(rectangle)}$' denotes area
• 'L' denotes length
• 'B' denotes breadth

We have,

• Area = 308 m²
• L = (x + 8) m
• B = x m

Putting all values,

➻ 308 = x × (x + 8) $\tt\qquad- (1)$

➻ 308 = x(x + 8)

➻ 308 = x² + 8x

➻ x² + 8x - 308 = 0

By splitting the middle term,

➻ x² + (22 - 14)x - 308 = 0

➻ x² + 22x - 14x - 308 = 0

➻ x(x + 22) - 14(x + 22) = 0

➻ (x + 22) (x - 14) = 0

➻ x + 22 = 0$\quad\Big|\quad$x - 14 = 0

➻ x = 0 - 22$\quad\Big|\quad$x = 0 + 14

➻ x = -22$\quad\Big|\quad$x = 14

$\Big[$ Breadth of rectangle can't be negative $\Big]$

$\Big[$ So, we will reject 'x = -22' $\Big]$

• Henceforth, breadth of rectangular plot (x) is 14 m.

Now,

• Finding it's length •

➻ Length of rectangle = (x + 8) m

Putting value of 'x',

➻ Length of rectangle = (14 + 8) m

➻ Length of rectangle = 22 m

• Henceforth, length of rectangular plot (x + 8) is 22 m.

Verification:

➻ 308 = x × (x + 8) $\tt\qquad\Big[From\:(1)\Big]$

➻ 308 = x(x + 8)

Putting value of 'x',

➻ 308 = 14(14 + 8)

➻ 308 = 14(22)

➻ 308 = 14 × 22

➻ 308 = 308

➻ LHS = RHS

Hence, Verified ✔

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