Question

If the length of a rhombus and its one diagonal is 25cm
and 14 cm respectively, find the length of the other
diagonal and the area of the rhombus 336​

Answer 1

Answer:

26cm

Step-by-step explanation:

AREA OF RHOMBUS=1/2×d1×d2

⇒336=1/2×25×d2

⇒336×2=25×d2

⇒672=25×d2

⇒d2=672/25

⇒d2=26

Answer 2

Answer:

• Length of 2nd diagonal is 48 cm.
• Area of the rhombus is 336 cm².

Step-by-step explanation:

Given that:

• Length of a rhombus is 25 cm.
• Length of 1st diagonal is 14 cm.

To find:

• Length of the 2nd diagonal.
• Area of the rhombus.

Formulas used:

• (Height)² = (Hypotenuse)² - (Base)²

• Area of the rhombus = 1/2(product of diagonals)

Let us assume:

• Let ABCD be the rhombus.

Then,

Length = BC = 25 cm

1st diagonal = BD = 14 cm

Solution:

We know that diagonals of a rhombus bisect each other at 90° to form right angle triangle, with sides as : OC, OB and CB

∵ OB = 1/2(BD) = (1/2 × 14) cm = 7 cm

By Pythagoras Theorem,

(OC)² = (CB)² - (OB)²

Substituting the values,

(OC)² = (25)² - (7)²

(OC)² = 625 - 49

(OC)² = 576

OC = √576

OC = 24

Hence, OC = 24 cm

Therefore, AC = 2(OC) cm = (2 × 24) cm = 48 cm

Hence, length of the 2nd diagonal is 48 cm.

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Now,

Area of the rhombus = 1/2(product of diagonals)

= (1/2 × BD × CA)

= (1/2 × 14 × 48)

= 336

Hence, the area of the rhombus is 336 cm².