Question

the area of a rombus is 100 cm2. if one of its diagnols is 40cm, find the length of the other diagonal

Answer 1

➠ GIVEN

Area of a rhombus is 100 cm²

• One length of Diagonal

• (d2) = 40 cm

➠ To - Find

Other length of Diagonal

• (d1 ) = ?

➠ Solution :-

➠ Formula used

Area of Rhombus

= d1 × d2 / 2

• Place given value here in this formula.

➻ 100 cm = d 1 × 40 cm / 2

➻ d 1 = 100 ×2 / 40

➻ d 1 = 200 /40

➻ d 1 = 5

➠ Therefore

Other length of Diagonal

• (d1 ) = 5 cm.

➠ Verification

➻ Area of Rhombus

= d1 × d2 / 2

• Place the given value here in this formula.

➻ Area of Rhombus

= 5 × 40 / 2

➻ Area of Rhombus = 200 / 2

➻ Area of Rhombus = 100

L.H.S = R.H.S

➠ Therefore our answer is correct

Answer 2

Given :

• Area of rhombus = 100 cm²

• Length of one diagonal = 40 cm

To Find :

• Length of other diagonal = ??

formula used :

${ \underline{ \boxed{ \bf{ \pink {Area \: of \: rhombus = \dfrac{1}{2} </p><p> × Product \: of \: diagonals}}}}}</p><p>$

Solution :

$: \implies \tt \: Area \: of \: rhombus = \dfrac{1}{2} × d_ 1× d_2$

$: \implies \tt \: 100 \: cm ^{2} = \dfrac{1}{2} × AC × DB$

$: \implies \tt \: 100 \: cm ^{2} = \dfrac{1}{2} × AC × 40 \: cm$

$: \implies \tt \: 100 \: cm ^{2} × 2 × \dfrac{1}{40 \sf cm} = AC$

$: \implies \tt \: 5 \: cm = AC$

$: \implies \tt \: AC = 5 \: cm.$

∴ Length of other diagonal is 5 cm.