Question

The perimeter of a rectangle is 42 metres and one of its diagonals is 15 metres
a) If length of one side is x metres what is the other side?
b) What is the relation between the sides of the rectangle and its diagonal?
c) Write a second-degree equation using the above data
d) Find the sides of the rectangle.

Answer 1

Step-by-step explanation:

a)Given,

Length of one side = x metre

perimeter= 42m

2× (l+b) = 42

2× (x+b) = 42

x+b = 21

b= 21-x

Thus the length of other side is (21-x) metre

b)

now,

using Pythagoras theorem

x^2 + (21-x)^2 = 15^2

this us the relation between the sides of the rectangle and its diagonal.

c)

x^2 + 441-42x + x^2 = 225

2x^2 -42x = 225-441

2x^2 -42x = -216

x^2 - 21x = - 108

x^2 -21x + 108= 0

this is the second degree equation

d)

x^2 - 12x - 9x +108=0

x(x-12) - 9(x-12)= 0

(x-12)(x-9) = 0

thus x = 12 or 9

Thus, when length =x= 12m

breadth = 21-x = 21-12= 9m

or, when length = x = 9m

breadth = 21-x = 21-9= 12m