Question

the sum of length, breadth and height of a cuboid is 19cm.the length of its diagonal is 11cm, find total surface area of the cuboid​

Answer 1

Answer:

240 cm²

Step-by-step explanation:

Let the length, breadth and height be l, b and h respectively.

Sum of length, breadth and height of the cuboid = 19

l + b + h = 19

[Assumed that sum of only one length, one breadth and one height of the cuboid is 19 cm. If any mistake, please inform me.]

The square of the diagonal of the cuboid is the sum of squares of one length, one breadth and one height of the cuboid.

∴ l² + b² + h² = 11²

⇒ l² + b² + h² = 121

The total surface area of the cuboid is 2(lb + bh + lh).

Let's find it.

(l + b + h)² = 19²

l² + b² + h² + 2(lb + bh + lh) = 361

121 + 2(lb + bh + lh) = 361

2(lb + bh + lh) = 361 - 121 = 240

∴ The answer is 240 cm².

Let me shorten the method!!!

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TO REMEMBER...

If the sum of the length, breadth and height, one of each, of a cuboid is s,

and the length of the diagonal of the cuboid is d,

then the total surface area of the cuboid is,

s² - d²             OR            (s + d)(s - d)

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Here,

s = 19

d = 11

s² - d² = 19² - 11² = 361 - 121 = 240

OR

(s + d)(s - d) = (19 + 11)(19 - 11) = 30 × 8 = 240

Hope this may be helpful.

Thank you. Have a nice day. :-)

#adithyasajeevan