Question

the ratio of two diagonals of rhombus of 2:3 if its area is 300sqcm find its two diagonals​

Answer 1

Answer:

hey here is your solution

pls mark it as brainliest

Step-by-step explanation:

so let two diahmals of rhombus be d1 and d2 respectively

so here d1:d2=2:3

let the common multiple be k

so d1=2k d2=3k

now we know that area of rhombus=1/2×d1×d2

thus here as area of rhombus=300

300=1/2×d1×d2

ie 2k×3k=600

so 6k square=600

ie ksquare=100

taking square roots on both sides we get

k=10 OR k=-10

but as diagonals dimensions of any geometric figure are never negative

k=-10 is absurd

so k=10

substitute it in 2k and 3k

you get 20 and 30 as final solution

thus length of two diagonals of rhombus are 20 cm and 30 cm

hope it helped u a lot

Answer 2

Given :

• Ratio of the two diagonals of the rhombus = 2 : 3

• Area of rhombus = 300 cm²

To find :

• The two diagonals

Solution :

Here, we have to find the two diagonals of the rhombus and we are given the ratio of them. So, firstly we shall assume the two diagonals according to the ratios given then by using the formula of area of rectangle we will find their values.

Let,

• First diagonal of the rhombus = 2x
• Second diagonal of the rhombus = 3x

Using formula,

→ Area of rhombus = ½ × D₁ × D₂

where,

• D₁ denotes the first diagonal

• D₂ denotes the second diagonal

Substituting the given values :-

→ 300 = ½ × 2x × 3x

→ 300 × 2 = 2x × 3x

→ 600 = 2x × 3x

→ 600 = 6x²

→ 600 ÷ 6 = x²

→ 100 = x²

→ Taking square root on both the sides :-

→ √100 = x

→ √(10 × 10) = x

→ ± 10 = x

→ As we know, the diagonal of rhombus cannot be negative. So, the negative sign will get rejected.

→ ± 10 Reject -ve = x

→ The value of x = 10

Substitute the value of x in the diagonals of rhombus :-

→ First diagonal = 2x

→ First diagonal = 2(10)

→ First diagonal = 20 cm

→ Second diagonal = 3x

→ Second diagonal = 3(10)

→ Second diagonal = 30 cm

Therefore, the diagonals of rhombus are 40 cm and 30 cm.