The area of a rhombus is equal to the area of a triangle with base 24.8 cm and altitude 16.5 cm.

Question

The area of a rhombus is equal to the area of a triangle with base 24.8 cm and altitude 16.5 cm. If one of the diagonals of the rhombus is 22cm, find the other diagonal.

Answer 1

area of the triangle

A=(1/2)bh

A=(1/2)(24.8)(16.5)

A=12.4*16.5

A=204.6 square centimeters for the area of the triangle

the diagonals of a rhombus divide the rhombus into 4 congruent triangles

the rhombus has the same area as the original triangle

the area of the rhombus is 204.6 square centimeters

each of the 4 congruent triangles has an area of 204.6/4=51.15 square centimeters

one diagonal is 22 cm

all 4 triangles are right triangles because the diagonals are perpendicular to each other

half of the diagonal is one leg and half of the other diagonal is the other leg and they are perpendicular to each other

these 2 half diagonals are the base and height of each of the 4 triangles

A=(1/2)(b)(h)

51.15=(1/2)(11)(h) where 11 is 22/2 and h is half of the other diagonal

multiply both sides by 2

102.3=11h

h=102.3/11

h=9.3 cm, which is half of the other diagonal

2*9.3=18.6 cm for the other diagonal