Question

The ratio of length, breadth and height of a rectangular solid is 3 : 2 : 1 and its total surface area is 352 sq. cm, then find the length.​???


No spam ✌️​

Answer 1

Answer:

length = 12 cm

Step-by-step explanation:

Step 1 of 4:

Given that:

Ratio of length: breadth: height = 3 : 2 : 1

Total surface of rectangular soild (TSA) = 352 $cm^{2}$

To find: Length of the rectangular soild.

Let the length $(l)$= $3x$; breadth $(b)$ = $2x$ and height $(h)$ = $x$.

The fomula to find (TSA):

$2(lb+bh+hl)$

Step 2 of 4:

Now substitute the values of length, breadth and height into the formula:

$352=2((3x\times2x)+(2x\timesx)+(x\times3x))\\352=2(6x^{2} +2x^{2} +3x^{2})\\352=2(11x^{2})\\352=22x^{2}$

Step 3 of 4:

Solve for $x$.

$x^{2}=\frac{352}{22} \\x^{2}=16$

Since $\sqrt{16}=\sqrt{4\times4} =4$

$x=4$

Step 4 of 4:

Finally substitute $x=4$ in length $(l)$= $3x$ to find the length.

$Length = 3x\\Length = 3(4)\\Length =12 cm$

Therefore length = 12 cm

Answer 2

length = 12 cm

Step-by-step explanation:

Step 1 of 4:

Given that:

Ratio of length: breadth: height = 3 : 2 : 1

Total surface of rectangular soild (TSA) = 352 cm^{2}cm

2

To find: Length of the rectangular soild.

Let the length (l)(l) = 3x3x ; breadth (b)(b) = 2x2x and height (h)(h) = xx .

The fomula to find (TSA):

2(lb+bh+hl)2(lb+bh+hl)

Step 2 of 4:

Now substitute the values of length, breadth and height into the formula:

\begin{gathered}352=2((3x\times2x)+(2x\timesx)+(x\times3x))\\352=2(6x^{2} +2x^{2} +3x^{2})\\352=2(11x^{2})\\352=22x^{2} \\\end{gathered}

352=2((3x×2x)+(2x\timesx)+(x×3x))

352=2(6x

2

+2x

2

+3x

2

)

352=2(11x

2

)

352=22x

2

Step 3 of 4:

Solve for xx .

\begin{gathered}x^{2}=\frac{352}{22} \\x^{2}=16\\\end{gathered}

x

2

=

22

352

x

2

=16

Since \sqrt{16}=\sqrt{4\times4} =4

16

=

4×4

=4

x=4x=4

Step 4 of 4:

Finally substitute x=4x=4 in length (l)(l) = 3x3x to find the length.

\begin{gathered}Length = 3x\\Length = 3(4)\\Length =12 cm\end{gathered}

Length=3x

Length=3(4)

Length=12cm

Therefore length = 12 cm