Question

the whole surface area of a rectangular block is 8788cm square if the length breadth and height are in the ratio 4:3:2 find the difference between it's length and height
the answer is 26 CM
I want the explanation please ​

Answer 1

Given :

• The whole Surface Area of a rectangular block is 8788 cm².
• Length , Breadth and Height are in the ratio 4:3:2.

To Find :

• Difference between length and height of block.

Solution :

$\longmapsto\tt{Let\:the\:Length\:of\:Block\:be=4x}$

$\longmapsto\tt{Let\:the\:Breadth\:of\:Block\:be=3x}$

$\longmapsto\tt{Let\:the\:Height\:of\:Block\:be=2x}$

Using Formula :

$\longmapsto\tt\boxed{Surface\:Area\:of\:Cuboid=2(lb+bh+hl)}$

Putting Values :

$\longmapsto\tt{8788=2(4x\times{3x}+3x\times{2x}+2x\times{4x)}}$

$\longmapsto\tt{8788=2({12x}^{2}+{6x}^{2}+{8x}^{2})}$

$\longmapsto\tt{8788=2({26x}^{2})}$

$\longmapsto\tt{\cancel\dfrac{8788}{2}=26{x}^{2}}$

$\longmapsto\tt{\cancel\dfrac{4394}{26}={x}^{2}}$

$\longmapsto\tt{\sqrt{169}=x}$

$\longmapsto\tt\bf{x=13}$

Value of x is 13...

Therefore :

$\longmapsto\tt{Length\:of\:Block=4(13)}$

$\longmapsto\tt\bf{52\:cm}$

$\longmapsto\tt{Breadth\:of\:Block=3(13)}$

$\longmapsto\tt\bf{39\:cm}$

$\longmapsto\tt{Length\:of\:Block=2(13)}$

$\longmapsto\tt\bf{26\:cm}$

Now ,

Difference between Length and Height of Block :

$\longmapsto\tt{Length-Height}$

$\longmapsto\tt{52-26}$

$\longmapsto\tt\bf{26\:cm}$