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Roman55 [17]
3 years ago
13

Volume of a rectangular prism.. PLEASE HELP

Mathematics
1 answer:
kondaur [170]3 years ago
7 0
\text {Volume = } \dfrac{5}{2x + 8}   \times  \dfrac{x+4}{4}  \times  \dfrac{12}{x}

---------------------------------------------------
Take out (x + 4) as a common factor :
---------------------------------------------------
\text {Volume = } \dfrac{5}{2(x + 4)}   \times  \dfrac{x+4}{4}  \times  \dfrac{12}{x}

---------------------------------------------------
Cross out (x + 4) :
---------------------------------------------------
\text {Volume = } \dfrac{5}{2}   \times  \dfrac{1}{4}  \times  \dfrac{12}{x}

---------------------------------------------------
Rewrite 12 as 4 x 3 :
---------------------------------------------------
\text {Volume = } \dfrac{5}{2}   \times  \dfrac{1}{4}  \times  \dfrac{4 \times 3}{x}

---------------------------------------------------
Cross out 4 :
---------------------------------------------------
\text {Volume = } \dfrac{5}{2}   \times  \dfrac{ 3}{x}

---------------------------------------------------
Combine into single fraction:
---------------------------------------------------
\text {Volume = } \dfrac{15}{2x}
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Answer:

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Step-by-step explanation:

Given that:

BC = 36 , CD = 15 and BD = x

As these are forming right angled triangle,

Using Pythagorean theorem,

(BD)^2+(CD)^2=x^2\\(36)^2+(15)^2 = x^2\\1296 + 225 = x^2\\1521 = x^2\\

Taking square root on both sides

\sqrt{x^2}=\sqrt{1521}\\x=39

As the given shape is rectangular, the sides parallel to each other will have same values.

AB = 15 , AD = 36 and AC = x

(15)^2+(36)^2 = x^2 \\225 + 1296 = x^2 \\1521 = x^2 \\x = 39

Now,

BD - AC = 39 - 39 = 0

Hence,

BD - AC = 0

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