Question

if the lengths of two diagonals are 4cm and 3cm ,find the area and the length of the side of the rhombus.

​

Answer 1

Answer:

Area of rhombus= $\rm{\green{6cm^2}}$

The length of side of the rhombus = 2.5cm

Step-by-step explanation:

Question:

If the lengths of two diagonals are 4cm and 3cm , find the area and the length of the side of the rhombus.

Given:

• $\sf{\pink{D_1}}$= 4cm
• $\sf{\blue{D_2}}$= 3cm

To find:

• Area of rhombus
• Length of the side of rhombus.

Solution:

Area = $\displaystyle\frac{D_1\times\:D_2}{2}$

Area= $\displaystyle\frac{4\times\:3}{2}$

$\displaystyle\frac{12}{2}$

Area = $\rm{\green{6cm^2}}$

Length of the side of the rhombus=

$\displaystyle\frac {\sqrt {p{}^{2} + q {}^{2}}}{2}$

$\displaystyle \frac{ \sqrt{4 {}^{2} + 3 {}^{2}}}{2}$

$\displaystyle\frac{5}{2}$= 2.5cm

Therefore, the length of side of the rhombus = 2.5cm

Final answer:

Area of rhombus= $\mathtt{\green{6cm^2}}$

The length of side of the rhombus = 2.5cm

Answer 2

Step-by-step explanation:

One diagonal of a rhombus is half the other. If the length of the side of the rhombus is 25 cm, what is the area of the rhombus?

Solution: Let the diagonals be 2x and 4x.

x^2+(2x)^2 = 25^2

5x^2 = 625, or

x^2 = 125, or

x = 5√5

The diagonals are 10√5 and 20√5

The area of the rhombus = (10√5)*(20√5)/2 = 500 cm^2. Answer