Question

the lbh of cuboid are in the ratio 1 ratio 2 ratio 3 and tsa is 352m square find lb and h​

Answer 1

Given:

• Ratio of cuboid = 1 :2 : 3
• Total Surface Area = 352$\sf{m}^{2}$

To Find:

• Length of cuboid = ?
• Breadth of cuboid = ?
• Height of cuboid = ?

Solution:

Let's assume:

• Let the length be x
• Let the breadth be 2x
• Let the height be 3x

As we know that,

$\Large{\sf{\fbox{\green{Total \:Surface\:Area = 2( Length × Breadth + Breadth × Height + Height × Length)}}}}$

According to the question,

$\sf \implies352 {m}^{2} =2( x \times 2x + 2x \times 3x + 3x \times x) \\ \\ \: \sf \implies \: 352 {m}^{2} = 2(2 {x}^{2} + 6 {x}^{2} + 3 {x}^{2} ) \\ \\ \: \: \sf \implies \: 352 {m}^{2} = 4 {x}^{2} + 12 {x}^{2} + 6 {x}^{2} \\ \\ \: \: \sf \implies \: 352 {m}^{2} = 22 {x}^{2} \\ \\ \: \: \: \sf \implies \: {x}^{2} = \cancel \frac { 352}{22} \\ \\ \: \: \sf \implies \: {x}^{2} = 16 \\ \\ \: \: \sf \implies \: x = \sqrt{16} \\ \\ \sf\dagger \therefore \: x = 4$

Hence,the value of x is 4.

Therefore,now find the value of Length , breadth and height.

• Length = x = 4
• Breadth = 2x = 2× 4 = 6
• Height = 3x = 3 × 4 = 12

$\Large{\sf{\red{\underline{know\:more\:info}}}}$

• Volume of Cuboid = Length × Breadth × Height
• Lateral surface area= 2h(l + b)
• Area of four walls of a room = 2 × h ×(l + b)

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$\Huge{\sf{\pink{\rightarrow{\purple{@Angelic\:Sparks}}}}}$

Answer 2

Answer:

l=4,b=8,h=12;

Step-by-step explanation:

Let l=x;

then,

b=2x;

h=3x;

NOW,

TSA = (lb+bh+hl);

352=2(x*2x+2x*3x+3x*x);

352/2=(2x^2+6x^2+3x^2);

176=11x^2;

176/11=x^2;

16=x^2;

√16=x;

4=x;

Putting value of x,

l=x=4;

b=2x=8;

h=3x=12;