Respuesta :
Length of the diagonal of rectangular prism is equals to 13units.
What is rectangular prism?
" Rectangular prism is a three dimensional figure which has six faces in rectangular shape."
Formula used
Total surface area of the rectangular prism = 2(l b + b h +l h)
Sum of all the edges of the prism = 4 (l +b + h)
length of the diagonal of the prism = √l² + b² + h²
l = length of the prism
b = width of the prism
h = height of the prism
According to the question,
Given,
Total surface area of the rectangular prism = 56 units
⇒2(l b + b h +l h) = 56
Sum of all the edges of the prism = 60 units
⇒4(l + b + h) = 60
Divide both the side by 4 we get,
(l + b + h) = 60 / 4
⇒(l + b + h) = 15 ____(1)
Squaring both the side of (1) we get,
(l + b + h)² = (15)²
⇒l² + b² + h² + 2 (l b + b h +l h) = 225
Substitute the value of total surface area to get length of the diagonal,
l² + b² + h² + 56 = 225
⇒l² + b² + h² = 225 - 56
⇒l² + b² + h² = 169
⇒√l² + b² + h² = √169
⇒√l² + b² + h² = 13
Hence, length of the diagonal of rectangular prism is equals to 13units.
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