Question

the length of a rectangle exceeds its width by 8 cm and the area of the rectangle is 240 square cm find the the dimensions of the rectangle

Answer 1

Answer:

12 cm by 20 cm

Step-by-step explanation:

Let the breadth of the given rectangle be x cm.  

Then, length =(x+8) cm

Now area =240cm  

2

 

⇒length×breadth=240⇒(x+8)x=240

⇒x  

2

+8x−240=0⇒x  

2

+20x−12x−240=0⇒(x+20)(x−12)=0

⇒x=12orx=−20

But x cannot be negative, So, x=12

Hence, length =x+8=12+8=20cm and breadth =12cm

Answer 2

Answer:

The dimensions of the rectangle are 20cm and 12 cm

Step-by-step explanation:

Given,

The length of the rectangle exceeds its width by 8cm.

Area of the rectangle = 240cm²

To find,

The dimensions of the rectangle

Recall the formula

Area of the rectangle = length× breadth

Let the length of the rectangle be 'l' and the breadth of the rectangle be 'b'.

The area of the rectangle = lb

we have,

lb = 240cm² ------------------(1)

Since it is given, the length of the rectangle exceeds its width by 8cm we have,

l = b+8

Substituting in equation (1) we get,

(b+8)b = 240

b² +8b- 240 = 0

b² +20b - 12b- 240 = 0

b(b+20) - 12(b+20) = 0

(b-12)(b+20) = 0

b= 12, b = -20

Since the breadth of a rectangle cannot be negative, we have b = 12

Length of the rectangle  = 12+8 = 20cm

∴ The dimensions of the rectangle are 20cm and 12 cm

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