Question

one of the diagonals of rhombus is thrice as the other . If the sum of the length of the diagonals is 24cm, then find the area of the rhombus.​

Answer 1

Answer:

54cm^2

Step-by-step explanation:

Let one of the diagonals of rhombus be ‘d1’ cm and the other be d2 cm.

Give d1 = 3 x d2

Also d1 + d2 = 24 cm

⇒ 3d2 + d2 = 24

4d2 = 24

d2 = 24/4

d2=6 cm

d1 = 3 x d2 = 3 x 6

d1 = 18 cm

∴ Area of the rhombus = 1/2 x d1 x d2 sq. units

= 1/2 x 18 x 6 cm2 = 54 cm2

Area of the rhombus = 54 cm2

Answer 2

Given

• One diagonal of rhombus is thrice as the other.
• Sum of length of the diagonals is 24 cm.

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To Find

• The area of the rhombus.

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Solution

Let one of the diagonal be 'x'.

The other diagonal would be '3x'.

We know that the sum of both diagonals is 24 so let's solve the following equation to find the value of the diagonals.

Let's solve your equation step-by-step.

x + 3x = 24

Step 1: Simplify the equation.

⇒ x + 3x = 24

⇒ 4x = 24

Step 2: Divide 4 from both sides of the equation.

⇒ 4x ÷ 4 = 24 ÷ 4

⇒ x = 6

∴ One diagonal ⇒ x = 6 cm

∴ Other diagonal ⇒ 3x = 3(6) = 18 cm

Now let's find the area of the rhombus with the obtained value of the diagonals.

Area of Rhombus ⇒ $\dfrac{d_1d_2}{2}$

(Here d₁ and d₂ are the diagonals)

Area of Given Rhombus ⇒ $\dfrac{6\times 18 }{2}$

Area of Given Rhombus ⇒ $\dfrac{108}{2}$

Area of Given Rhombus ⇒ 54 cm²

∴ The area of the given rhombus is 54 cm²

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