# What will be the length of the Hypotenuse of the Table? If

The perimeter of a top surface of a rectangular table is 28 m and its area is 48 m^{2}. What is the length of the hypotenuse of the table?

- 12.5m
- 5 m
- 10 m
- 12 m

**Answer: (3) 10 m**

**Explanation:-
**The perimeter of a top surface of e rectangular table = 28 m

**Formula-
The perimeter of the rectangular table = 2 (l + b)**

Then, 2(l + b) = 28

l + b = 28/2

l + b = 14 ……………………………………………….. (1)

Area of surface of the rectangular table = 48 m^{2}

Then, lb = 48

l = 48/b

Put the value of l = 48/b in equation (1),

Then, 48/b + b = 14

(48 + b^{2}) /b = 14

48 + b^{2} = 14b

b^{2} – 14b + 48 = 0

b^{2} – 8b – 6b + 48 = 0

b (b – 8) – 6 (b – 8) = 0

(b – 8) (b – 6) = 0

b – 8 = 0 & b – 6 = 0

b = 8 & b = 6

Then, l = 48/6 = 8

l = 8 cm & b = 6 m

Hypotenuse of the rectangular surface of the table = (8^{2} + 6^{2})^{1/2}

= (64 + 36)^{1/2}

= (100)^{1/2}

= 10 m

Then, the hypotenuse of the table is 10 m.

Hence, the answer is (3) 10 m.