The length of one side of rhombus is 52cm. Ine of its daigonals is 40cm. Find the lenght of the other daigonal and the area of the rhombus

Question

This questions is related to Pythagoras theorem... area of rhombus is required. 

Answer 1

draw a rhombus and its diagonals

the diagonals bisect each other and are perpendicular to each other

the diagonals form four right triangles

choose one

the hypotenuse is one of the sides of the rhombus, 52 cm

one leg of the triangle is 1/2 of 40 which is 20

the other leg, which is half of the other diagonal, is unknown so call it "d"

52²=20²+d²

2704=400+d²

d²=2704-400

d²=2304

d=√2304

d=48 cm

therefore, the other diagonal is 2*48=96 cm

the formula for the area of a rhombus is...

A=(1/2)*diagonal1*diagonal2

A=(1/2)*40*96

A=20*96

A=1920 sq cm for the area of the rhombus