Question

find the length of the altitude of the rhombus if length of its two diagonals are 12cm and 16 cm respectively

Answer 1

all sides of a rhombus are equal in length.

the diagonals of the rhombus intersect at a 90 degree angle.

the diagonals and the sides of the rhombus form right triangles.

one leg of these right triangles is equal to 8 cm in length.

the other leg of these right triangles is equal to 6 cm in length
that would be half the length of each diagonal.

the sides of the triangle form the hypotenuse of these right triangles.

the formula is:

hypotenuse squared = one leg squared plus other leg squared.

this makes the hypotenuse squared equal to 8^2 + 6^2 = 64 + 36 = 100

the hypotenuse is the square root of 100 which makes the hypotenuse equal to 10.

the sides of the rhombus are equal to 10 cm.

Answer 2

Answer:

Altitude = 9.6 cm

Step-by-step explanation;

The diagonal of the rhombus bisect each other at right angle.

So, by Pythagoras Theorem, you can calculate one of the side of the rhombus,

6^2+8^2 = (Hypotenus or side of rhombus)^2

   √100  = Side of Rhombus

Side of Rhombus = 10cm

Rhombus can be called as parallelogram, so

Area of Parallelogram = Area of Rhombus

Base * Altitude= 1/2 (product of the length of the diagonals)

10*Altitude= 1/2 (12*16)

On solving,

Altitude = 6*16/10

             = 9.6 cm