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3 years ago

A cuboid with a volume of 374cm^3 has dimensions

Mathematics

2 answers:

Cloud [144]3 years ago

5 0

Step-by-step explanation:

Part 1)

The equation by factorization is

x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))x

+12x−230=(x−(−6+

266

))(x−(−6−

266

))

Both values of x are

x1=-6+\sqrt{266}x1=−6+

266

x2=-6-\sqrt{266}x2=−6−

266

Part 2) The dimensions of the cuboid are

4\ cm4 cm , (-5+\sqrt{266})\ cm(−5+

266

) cm and (5+\sqrt{266})\ cm(5+

266

) cm

Step-by-step explanation:

step 1

we know that

The volume of the cuboid is equal to

V=LWHV=LWH

substitute the given values

V=4(x+1)(x+11)V=4(x+1)(x+11)

V=924\ cm^{3}V=924 cm

\begin{gathered}4(x+1)(x+11)=924\\4(x^{2}+11x+x+11)=924\\ 4(x^{2}+12x+11)=924\\x^{2}+12x+11=231\\x^{2}+12x-230=0\end{gathered}

4(x+1)(x+11)=924

4(x

+11x+x+11)=924

4(x

+12x+11)=924

+12x+11=231

+12x−230=0

Complete the square

x^{2}+12x-230=0x

+12x−230=0

x^{2}+12x=230x

+12x=230

x^{2}+12x+36=230+36x

+12x+36=230+36

(x+6)^{2}=266(x+6)

=266

square root both sides

x+6=(+/-)\sqrt{266}x+6=(+/−)

266

x=-6(+/-)\sqrt{266}x=−6(+/−)

266

x1=-6+\sqrt{266}x1=−6+

266

x2=-6-\sqrt{266}x2=−6−

266

therefore

The equation by factorization is

x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))x

+12x−230=(x−(−6+

266

))(x−(−6−

266

))

step 2

Find the dimensions of the cuboid

The dimensions are

4\ cm4 cm

(x+1)\ cm ----- > (-6+\sqrt{266}+1)=(-5+\sqrt{266})\ cm(x+1) cm−−−−−>(−6+

266

+1)=(−5+

266

) cm

(x+11)\ cm ---- > (-6+\sqrt{266}+11)=(5+\sqrt{266})\ cm(x+11) cm−−−−>(−6+

266

+11)=(5+

266

) cm

kkurt [141]3 years ago

5 0

Answer:

2 x 11 x 17 = L x W x H

Step-by-step explanation:

x² + 12 (8) - 160 = 0

8(8) + 96 -160 = 0

8(8) + 96 -160

160 -160 = 0

x² + 12x -160 = 0

x² + 8 × - 20 = 0

(x +8) (x-20)

2( x+3 ) × (x+9) = 374

(x+3) × (x+9) = 374 ÷ 2

(x+3)× (x+ 9) = 187

x² = 184 - 9

x² = 175

x = 175/25

x = 8

Formula of Volume of Cuboid

V = L ×W × H

V = 2 × (x+3) × (x+9)

2 ( 8+3 ) × ( 8+ 9)

2 (11) × (17)

x + 3 = 11

x + 9 = 17

Volume L × W × H

2 × 11 × 17 = 374cm³

satisfies the equation

dimensions of the cuboid

2 11 and 17

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d) See the graph below

=========================================================

Explanations:

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-----------------------

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-----------------------

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-----------------------

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