Question

If a, b and c are length, breadth and height of a cuboid and a + b + c = 10cm and a2 + b2 + c2 = 40cm2, find the surface area of the cuboid?

Answer 1

Answer:

60 cm²

Step-by-step explanation:

a + b + c = 10 cm

a² + b² + c² = 40 cm²

We know that the surface area of a cuboid is given by :

2 ( ab + bc + ca )

Now :

( a + b + c )² = a² + b² + c² + 2 ( ab + bc + ca )

⇒ 10² = 40 + 2 ( ab + bc + ca )

⇒ 2 ( ab + bc + ca ) = 100 - 40

= 60 cm²

Answer 2

▶ Question :-

→ If a, b and c are length, breadth and height of a cuboid and a + b + c = 10cm and a² + b² + c² = 40cm² , find the surface area of the cuboid?


▶ Answer :-

→ 60 cm² .


▶ Step-by-step explanation :-


➡ Given :-

→ a + b + c = 10 cm .

→ a² + b² + c² = 40 cm² .


➡ To find :-

→ Surface area of cuboid i.e., = 2( ab + bc + ca ) .


$\huge \pink{ \underline{ \underline{ \tt Solution :- }}}$

We have ,

→ a + b + c = 10 cm .

→ a² + b² + c² = 40 cm² .



▶ Now, using Identity :-

( A + B + C )² = A² + B² + C² + 2( AB + BC + CA ) .

==> ( 10 )² = 40 + 2( ab + bc + ca ) .

==> 100 = 40 + 2( ab + bc + ca ) .

==> 2( ab + bc + ca ) = 100 - 40 .

•°• 2( ab + bc + ca ) = 60 cm² .


✔✔ Hence, surface area of cuboid is 60 cm² ✅✅ .


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