Question

The length of a verandah is 3 m more than
its breadth. The numerical value of its area is
equal to the numerical value of its perimeter.
Find the dimensions of the verandah.​

Answer 1

Answer:

Heya!!

Given :-

• The length of a verandah is 3 m
• more than its breadth
• The numerical value of its area is
• equal to the numerical value of its perimeter.

To Find :-

• Find the dimensions of the verandah.

Supposed

• breadth = x
• length = (3 + x)

Area = Perimeter

length × breadth = 2 (length + breadth)

(3+x) (x) = 2 (3+x+x)

3x+ x² = 2 (3+2x)

3x + x² = 6 + 4x

x² + 3x- 4x - 6 = 0

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x (x-3) + 2 (x-3) = 0

(x+2) (x-3) = 0

⇒ x = 3,

because - it is not possible

• ∴ l = 3 + x = 3+3 = 6

Hence breadth = 3m and length = 6m

Answer 2

Answer:

Step-by-step explanation:

Verandah = rectangle

Perimeter of rectangle = 2(l+b)

Area of rectangle = lb

In the question,

l = b +3

And P = A

Therefore,

2(l + b) = lb

2[(b+3) + b] = (b + 3)b

=> 2(2b + 3) = b² + 3b

=> 4b + 6 = b² + 3b

=> b² + 3b - 4b - 6 = 0

=> b² -b -6 = p

=> b² -3b + 2b - 6 = 0

=> b(b - 3) + 2(b - 3)

=> (b - 3) = 0 and (b + 2) =0

=> b = 3 and -2

b can not be negative. Therefore we take the positive value

∴b = 3cm

And, l = b + 3

=3 + 3

= 6cm

Length = 6cm; breadth = 3cm