Question

2. Find the length of one diagonal of a rhombus if:
a. the other diagonal is 7 m and the area is 42 sq.m.
b. the other diagonal is 28 cm and the area is
504 sq.cm.​

Answer 1

Here, In all questions we have to find other diagonal of rhombus where one diagonal and area of rhombus is given.

We know,

$\boxed{\sf \bold{Area \: of \: rhombus = \dfrac{1}{2} \times d_{1} \times d_{2}}}$

Where,

• d₁ and d₂ are Diagonals of rhombus.

Answer (A) :-

Area = 42 m²

d₁ = 7 m.

Put all values in area formula :

$\longrightarrow$ 42 = 1/2 × d₁ × d₂

$\longrightarrow$ 42 = 1/2 × 7 × d₂

$\longrightarrow$ 42 × 2 = 7 × d₂

$\longrightarrow$ 84 = 7 × d₂

$\longrightarrow$ 84/7 = d₂

$\longrightarrow$ d₂ = 12

Thus,

Other diagonal of rhombus is 12 m.

Answer (B) :-

Area = 504 cm²

d₁ = 28 cm

Put all values in area formula:

$\longrightarrow$ 504 = 1/2 × d₁ × d₂

$\longrightarrow$ 504 = 1/2 × 28 × d₂

$\longrightarrow$ 504 × 2 = 28 × d₂

$\longrightarrow$ 1008 = 28 × d₂

$\longrightarrow$ 1008/28 = d₂

$\longrightarrow$ d₂ = 36

Thus,

Other diagonal of rhombus is 36 cm.

Answer 2

⚡Solution:-

a)

• We have area of rhombus =42 sq.m
• Length of other diagonal (D)=7m

To find length of one diagonal (d) we will apply the formula

➠Area of rhombus = 1/2 ×d×D

⇒Area of rhombus = 1/2×d × 7

⇒42 =7/2 d

⇒d=42×2/7

⇒d=12 m

Verification:—

________________

• Area of rhombus =1/2×d×D
• Area of rhombus =1/2×12×7
• Area of rhombus = 42 sq. m

________________

b)

• We have given area of rhombus = 504 sq.cm
• Length of other diagonal (D)=28cm

Let d be the length of diagonal which we have to find out , now again applying same formula

➠Area of rhombus =1/2×d×D

⇒Area of rhombus =1/2 ×d×28

⇒504=14 d

⇒= 504/14

⇒d=36 cm

Verification:—

________________

• Area of rhombus =1/2×d×D
• Area of rhombus =1/2×36×28
• Area of rhombus = 504 sq.cm

________________