Question

Find the area of a rhombus whose side is 6.5cm and altitude is 5cm.If one of its diagonal is 13 cm long, find the length of other diagonal.​

Answer 1

Step-by-step explanation:

A square plate of side 15 mis placed horizontally 2m below the surface of water. The atmospheric pressure is 1.1254 x 105 Nm-2. Calculate the total thrust on the plate.

(Given : Density of water = 103 kg m-3, g= 9.8 ms-1)

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Side of a rhombus, (s) = 6.5 cm
• Height of rhombus, (h) = 5 cm
• One diagonal of rhombus, (d1) = 13 cm

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of rhombus a/q to the given question.

$\mapsto\sf{Area \:of\:rhombus = 2 \times area \:of\:\triangle \:ABC}$

$\mapsto\sf{Area \:of\:rhombus = 2 \times \dfrac{1}{2} \times Base \times Height}$

$\mapsto\sf{Area \:of\:rhombus = 2 \times \dfrac{1}{2} \times 6.5 \times 5}$

$\mapsto\sf{Area \:of\:rhombus = \cancel{\dfrac{2}{2}} \times 6.5 \times 5}$

$\mapsto\sf{Area \:of\:rhombus =( 1 \times 6.5 \times 5)\:cm^{2}}$

$\mapsto\bf{Area \:of\:rhombus =32.5\:cm^{2}}$

Now,

As we know that formula of the area of rhombus;

$\boxed{\bf{Area = \frac{1}{2} \times d_1 \times d_2 }}$

$\longrightarrow\tt{Area\:_{(rhombus)} = \dfrac{1}{2} \times d_1 \times d_2}$

$\longrightarrow\tt{32.5= \dfrac{1}{2} \times 13 \times d_2}$

$\longrightarrow\tt{32.5 \times 2 = 13 \times d_2}$

$\longrightarrow\tt{65 = 13 \times d_2}$

$\longrightarrow\tt{d_2 = \cancel{65/13}}$

$\longrightarrow\bf{d_2 = 5\:cm}$

Thus,

The length of the other diagonal will be 5 cm .