Question

$\frac{x}{25} = \frac{196}{x}$
What is the value of x?​

Answer 1

Answer:

• The value of x is 70

Step-by-step explanation:

Given,

• $\tt\frac{x}{25} = \frac{ {196} }{x}$

To Find,

• The value of x.

Solution,

$:\implies \tt \frac{x}{25} = \frac{196}{x} \\ \\ :\implies \tt {x}^{2} = 196 \times 25 \\ \\ :\implies \tt {x }^{2} = 2 \times 2 \times 7 \times 7 \times 5 \times 5 \\ \\ :\implies \tt {x}^{2} = {(2 \times 7 \times 5)}^{2} \\ \\ :\implies \tt {x} = 2 \times 7 \times 5 \\ \\ :\implies \color{red} \boxed{ \tt x = 70}$

Verification,

$:\implies \tt \frac{x}{25} = \frac{196}{x} \\ \\ :\implies \tt \frac{70}{25} = \frac{196}{70} \\ \\:\implies \tt \frac{14}{5} = \frac{14}{5} \\ \\ :\implies \tt LHS = RHS$

Required Answer,

• The value of x is 70.

Answer 2

Answer:

Answer:

The value of x is 70

Step-by-step explanation:

Given,

\begin{gathered} \tt\frac{x}{25} = \frac{ {196} }{x} \\ \end{gathered}

25

x

=

x

196

To Find,

The value of x.

Solution,

\begin{gathered}:\implies \tt \frac{x}{25} = \frac{196}{x} \\ \\ :\implies \tt {x}^{2} = 196 \times 25 \\ \\ :\implies \tt {x }^{2} = 2 \times 2 \times 7 \times 7 \times 5 \times 5 \\ \\ :\implies \tt {x}^{2} = {(2 \times 7 \times 5)}^{2} \\ \\ :\implies \tt {x} = 2 \times 7 \times 5 \\ \\ :\implies \color{red} \boxed{ \tt x = 70}\end{gathered}

:⟹

25

x

=

x

196

:⟹x

2

=196×25

:⟹x

2

=2×2×7×7×5×5

:⟹x

2

=(2×7×5)

2

:⟹x=2×7×5

:⟹

x=70

Verification,

\begin{gathered}:\implies \tt \frac{x}{25} = \frac{196}{x} \\ \\ :\implies \tt \frac{70}{25} = \frac{196}{70} \\ \\:\implies \tt \frac{14}{5} = \frac{14}{5} \\ \\ :\implies \tt LHS = RHS\end{gathered}

:⟹

25

x

=

x

196

:⟹

25

70

=

70

196

:⟹

5

14

=

5

14

:⟹LHS=RHS

Required Answer,

The value of x is 70.

hope it helps you