Question

If the top of a rectangular table has an area of 35 in.², and its dimensions have a sum of 12, what are the dimensions?

Answer 1

Answer:

5 m and 7 m

Step-by-step explanation:

Given :

• The top of a rectangular table has an area of 35 m²
• The sum of the dimensions is 12

To find :

the dimensions

Solution :

Let the length of the rectangular table be 'l'

and breadth of the rectangular table be 'b'

Their sum = 12

l + b = 12

l = (12 – b)

We know that,

Area of the rectangle = length × breadth

35 = l × b

35 = (12 – b) × b

35 = 12b – b²

b² – 12b + 35 = 0

Solving this quadratic equation by splitting middle term,

b² – 5b – 7b + 35 = 0

b(b – 5) – 7(b – 5) = 0

(b – 5) (b – 7) = 0

b = 7 , 5

If breadth = 5 m,

length = (12 – 5) m = 7 m

If breadth = 7 m,

length = (12 – 7) m = 5 m

Therefore, the dimensions of the rectangle are 5 m and 7 m