Question

Find the length of the shorter diagonal of a rhombus if:

Answer 1

a) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

Let diagonal (D2 )= longer diagonal = 15 and diagonal (D1) = shorter diagonal

90 = ½ (D1)*15

90 = 7.5 D1

Now divide both side by 7.5

90/7.5 = d1

D1= 12 units.

b) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

Let the ratio be $x$

Diagonal 1= $2x$

Diagonal 2= $3x$

147 = ½ * $(2x)*(3x)$

Multiply both side by 2

294 = $(2x)*(3x)$

294 = 6$x^2$

Divide both side by 6

294/6 = 6$x^2$/6

49 = $x^2$

$x$= 7 unit