Question 3.

If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the quadrilateral?

Solution:

Let ₹ABCD be the rhombus. Diagonals AC and BD intersect at point E.

In ∆ADE,

m ∠AED = 90° …[Diagonals of a rhombus are perpendicular to each other]

∴ [l(AD)]² = [l(AE)]² + [l(DE)]² … [Pythagoras theorem]

∴ (25)² = (24)² + l(DE)² … [From (ii) and (iii)]

∴ 625 = 576 + l(DE)²

∴ l(DE)² = 625 – 576

∴ l(DE)² = 49

∴ l(DE) = √49

… [Taking square root of both sides]

Question 4.

If length of a diagonal of a rhombus is 30 cm and its area is 240 sq.cm, find its perimeter.

Solution:

Let ₹ABCD be the rhombus.

Diagonals AC and BD intersect at point E.

l(AC) = 30 cm …(i)

and A(₹ABCD) = 240 sq. cm .. .(ii)

In ∆ADE,

m∠AED = 90°

…[Diagonals of a rhombus are perpendicular to each other]

∴[l(AD)]² = [l(AE)]² + [l(DE)]²

…[Pythagoras theorem]

∴l(AD)² = (15)² + (8)² … [From (iv) and (v)]

= 225 + 64

∴l(AD)² = 289

∴l(AD) = √289

…[Taking square root of both sides]

∴l(AD) = 17 cm

Perimeter of rhombus = 4 × side

= 4 × l(AD)

= 4 × 17

= 68 cm

∴The perimeter of the rhombus is 68 cm.