Question

Lateral surface area of a cuboid is 486 Cm². It's brea is 12m and length and height are in the ratio 5:3. Fir the length and height of the cuboid.​

Answer 1

Given,

Lateral surface area of a cuboid $=486cm^{2}$

Breadth of cuboid $=12cm$

Length and height are in the ratio $5:3$

The length of cuboid be $5x$

The height of cuboid be $3x$

Formula for lateral surface area

$A=2h(l+b)$

$486=2\times3x(5x+12)$

$486=6x(5x+12)$

$81=5x^{2} +12x$

$5x^{2} +12x-81=0$

$5x-15x+27x-81=0$

$5x(x-3)+27(x-3)=0$

$(x-3)(5x+27)=0$

$x=3,x=-\frac{27}{5}$

Since, $x=3$ and $-\frac{27}{5}$ is not considered as length and height should not be negative values.

$x=3$

Length $=5x=15 cm$

Height $=3x=9cm$

Therefore, length $= 15cm$

breadth$= 9cm$.

Answer 2

Answer:

Length of the cuboid $=15m$ and height of the cuboid $=9m$

Step-by-step explanation:

Given data,

• Lateral surface area of a cuboid $=486cm^{2}$

• Breadth of the cuboid $=12m$

• The length and height of the cuboid are in the ratio $5:3$

As we know, lateral surface area of a cuboid $2h(l+b)$

Let the length and height of the cuboid be $5x$ and $3x$ respectively

So,

Area of the cuboid $=2\times3x(5x+12)$

$\Rightarrow 81=5x^{2}+12x$

$\Rightarrow 5x^{2}+12x-81=0$

$\Rightarrow 5x^{2}-15x+27x-81=0$

$\Rightarrow 5x(x-3)+27(x-3)=0$

$\Rightarrow (x-3)(5x+27)=0$

$\Rightarrow x=3,-\frac{27}{5}$

$x$ can not be negative

So, the value of $x=3$

Therefore, length of the cuboid $=5\times3=15m$

and height of the cuboid $3\times3=9m$.