Question

The area of the rhombus with one diagonal 18 cm long is same as the area of a square with side 15 cm. Find the length of the other diagonal of the rhombus.

Answer 1

Given :-

• One diagonal of rhombus = 18 cm
• Side of square = 15 cm
• Area of rhombus = Area of square

To find:-

Other diagonal of rhombus = ?

Solution:-

⋆ DIAGRAM OF RHOMBUS:-

$\setlength{\unitlength}{1 cm}}\begin{picture}(12,4)\thicklines\put(5,7){ . }\put(6,6){\line(1,0){3}}\put(7,9){\line(1,0){3}}\put(6,6){\line(1,3){1}}\put(9,6){\line(1,3){1}}\put(6,6){\line(4,3){4}}\put(9,6){\line(-2,3){2}}\put(5.6,5.9){ B }\put(9.1,5.9){ C }\put(6.6,8.9){ A }\put(10.1,8.9){ D }\put(6.8,7.2){ 18\:cm }\end{picture}$

As we know,

☛ Area of rhombus = ½ × d1 × d2

Let the other diagonal be d"

→ Area of rhombus = ½ × 18 × d"

→ Area of rhombus = 9(d")

$\rule{200}{1}$

⋆ DIAGRAM OF SQUARE:-

$\setlength{\unitlength}{1.05 cm}}\begin{picture}(12,4)\thicklines\put(5.6,9.1){ A }\put(5.6,5.8){ B }\put(9.1,5.8){ C }\put(9.05,9.1){ D }\put(4.5,7.5){ 15\:cm }\put(7.1,5.3){ 15\:cm }\put(9.5,7.5){ 15 \:cm }\put(7.1,9.5){ 15 \:cm }\put(6,6){\line(1,0){3}}\put(6,9){\line(1,0){3}}\put(9,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\end{picture}$

Now we know,

☛ Area of square = (Side)²

→ Area of square = (15)² cm²

→ Area of square = 225 cm²

A/q,

→ 225 = 9(d")

→ d" = 225/9

→ d" = 25 cm

Therefore,

Other diagonal of rhombus is 25 cm.