Question

ABCD is a rhombus in which length of diagonal is 48 cm and side is 25 cm. Find the sum
of the length of diagonals.​

Answer 1

diagonal of a rhombus are perpendicular to each other

In triangle ABCD , we have:

AC= 48cm

BD=25cm

so,by pytagores therome , we have:

BO=square root [(25)2-(48)2]=1679cm

Also , the diagonal of a rhombus bisect each other

so,AC=2AO=48 cm

and BD=2BO=2,819,041cm

thus sum of lengths of diagonal = 48cm+2,819,041cm= 2,819,089cm

Answer 2

Given:-

• Length of Diagonal = 48cm

• Length of Sides = 25cm

To Find:-

• The Length of Diagonal.

Construction:-

• Draw a Rhombus ABCD.

• Make Diagonal from A to C and another Diagonal from B to D.(See Fig).

Conecpt Used:-

• In Rhombus, All the Sides are equal.

• Diagonals Bisect each other at right angled triangle.

• Pythogoras theorem.

Now,

AB = BC = CD = AD = 25cm

&

BD = 48cm

In Right angles ∆BOC.

→(BO)² + (CO)² = (BC)²

• In this, BO = BD/2 = 24cm

→ (24)² + (CO)² = (25)²

→ 576 + (CO)² = 625

→ (CO)² = 625 - 576

→ (CO)² = 49

→ √(CO)² = √49

→ CO = 7cm.

Therefore,

→ AC → 2CO → 2 × 7 → 14cm.

Hence, The Diagonal AC is 14cm.

Atq.

Sum of the Diagonal = BD + AC → 48 + 14 → 62cm.

Hence, The Sum of the Diagonal is 62cm.