Question

The length of one side of the rhombus is 41 cm and its area is 720 cm^2. What is the sum of the length of its diagonals

Answer 1

In a rhombus diagonals bisect each other at right angle i.e 90°

Suppose diagonal1= a and digonal2= b

Diagonals will divide rhombus into 4 right angled triangle of equal area. Thus applying pythagorus theorem in one of the triangle,

[(a/2)^2 ] + [(b/2)^2 ] = 41^2

a^2 + b^2 = 6724 ——- equation-1

{Area of a rhombus is = (1/2)* a * b where a and b are diagonals of the rhombus}

Thus, (1/2)*a*b = 720

Therefore, a*b = 1440 ——— equation-2

As we know that,

(a+b)^2 = (a^2 + b^2 + 2*a*b)

Substituting value from equation 1 and 2 we will get,

(a+b)^2 = 6724+2880 = 9604

(a+b) = 98 { a+b gives sum of diagonals}