Question

Find the perimeter of a rhombus whose diagonals are 20cm and 48 cm.

Answer 1

perimeter will be 104 cm

Answer 2

Answer:

Step-by-step explanation:

You extract a right angled triangle because its diagonals meet at an angle of 90 degrees.

Now that you've extracted a right angled triangle, you find the hypotenuse (the side of the rhombus) because you have the base and height.

The  height of the triangle is 20/2 = 10cm while the base of the triangle is 48/2 = 24cm

a² + b² = c²

10² + 24² = c² ( we remove units in order not to be confused in the end.)

(10 * 10) + (24 * 24) = c²

100 + 576 = c²

√676 = √c² ( find the square root on both sides where by the square sign goes with the sign for square root)

Then you prime factorize 676 which is 26

That means the side of the rhombus is 26cm

So you find the perimeter

P = 4s

P = 4 * s

P = 4 * 26cm

P = 104cm