Sum of length breadth height of a cuboid=25
Total surface area 2(lb +bh + lh) =264
Find the area of the square on the diagonal of the cuboid. What is the length of the diagonal of the cuboid?
Answers
The length of the diagonal of the cuboid is 19 cm and the area of the square on the diagonal of the cuboid id 361 cm².
Step-by-step explanation:
Step 1:
Let the length, breadth and height of the cuboid be “l”, “b” & “h” respectively.
It is given, sum of length, breadth & height of the cuboid = 25 cm
So,
l+b+h = 25
squaring both sides
⇒ [l+b+h]² = 25²
⇒ l² + b² + h² + 2(lb +bh + lh) = 625
substituting Total surface area of cuboid = 2(lb +bh + lh) = 264 cm² [given]
⇒ l² + b² + h² + 2(lb +bh + lh) = 625
⇒ l² + b² + h² + 264 = 625
⇒ l² + b² + h² = 361 ….. (i)
Step 2:
We know that the formula for the length of the diagonal of the cuboid is given by,
d = √[l² + b² + h²]
⇒ d = √[361] …… []substituting from (i)]
⇒ d = 19 cm
Step 3:
Since it is given that the square is on the diagonal of the cuboid, so the length of each side of the square is equal to the diagonal of the cuboid i.e., 19 cm.
Therefore,
The area of the square on the diagonal of the cuboid is given by,
= side²
= 19²
= 361 cm²
Thus, the length of the diagonal of the cuboid is 19 cm and the area of the square on the diagonal of the cuboid is 361 cm².
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