Question

A rectangular carpet has an area of 120 sq.m and a perimeter of 46 m. Thge length of its diagonal (in metres) is:
a. 11
b. 13
c. 15
d. 17

Answer 1

the answer is 13 meter

Answer 2

Define x and y:

Let x and y be the two sides of the rectangle

Form equation 1:

Perimeter = 2(Length + Breadth)

46 = 2( x + y)

23 = x + y

x = 23 - y ------------- [ 1 ]

Form equation 2:

Area = Length x Breath

xy = 120 ------------- [ 2 ]

Sub [ 1 ] into [ 2 ]:

y (23 - y) = 120

23y - y² = 120

y² - 23y + 120 = 0

(y - 8) (y - 15) = 0

y = 8 or y = 15

⇒ The length is 15 cm and the breadth is 8 m

Find the diagonal:

a² + b² = c²

c² = 8² + 15²

c² = 289

c = √289

c = 17 m

Answer: (d) 17 m