Question

$\Large{\underline{\underline{\bf{Question:-}}}}$

find the side of a cube whose L.S.A is 196cm2​

Answer 1

Answer:

Answer:-

side of the cube is $\boxed{\red{7cm }}$

Solution:-

Lateral Surface Area = 196 cm²

Let the side be = y

According to Question:-

$\: \boxed{\sf{Lateral \: Surface \: Area \: of \: Cube = {4s}^{2} }}$

$\sf{\longrightarrow} \: 4 {y}^{2} = 196$

$\sf{\longrightarrow} \: {y}^{2} = \dfrac{196}{4}$

$\sf{\longrightarrow} \: {y}^{2} = 49$

$\sf{\longrightarrow} \: y = \sqrt{49}$

$\sf{\longrightarrow} \: y = \sqrt{7 \times 7}$

$\sf{\longrightarrow} \: y = 7$

Side = 7 cm

∴ the side of the cube is 7 cm

Answer 2

$\huge{ \sf \color{lightgrey}{answer} \color{lightpink}{\ :}}$

let the side of the cube be a cm.

$\begin{aligned} \qquad&lsa = 196 &cm^{2} \\ \implies&4 {a}^{2} = 196 &{cm}^{2} \\ \implies& {a}^{2} = \frac{ \cancel{196} \ {}^{49} }{ \cancel4 \ _{1}} &{cm}^{2} \\ \implies& \sqrt{ {a}^{2} } = \sqrt{49} &cm {}^{ \ \ } \\ \implies&a = 7 &cm {}^{ \ \ }\end{aligned}$

$\\ \\ \\ \boxed{\sf \quad side = 7 \: cm \quad } \\ \\ \\ \\ \\ \\ \\ \sf☆ \: Thank \: You! \: ☆$