A box is 1 meter wider than its height and 2 meters longer than his width.
1 answer:
Let the height be
Hence, the width is $x+1$ and length is $(x+1)+2=x+3$
The volume is given to be 2 m³
Hence, $2=x(x+1)(x+3)$
Solving,
$x^3+4x^2+3x-2=0$
$(x+2)(x^2+2x-1)=0$
$\implies x+2=0$ or $x^2+2x-1=0$
But $x=-2$ cannot be possible
Hence, $x^2+2x-1=0$
$\implies x=-1-\sqrt 2$ or $x=-1+\sqrt 2$
Reject the negative solution.
Hence, the height is $\sqrt 2-1$,
width is $\sqrt 2$ and length is $\sqrt 2 +2$
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Step-by-step explanation:
We know that we have a 9 foot long ladder resting upon a wall, with an unknown height, but the ladder is 4.5 feet away from the wall.
This can be represented as a triangle, where x is the unknown side.
|\
| \
x | \ 9
| \
| \
|_____\
4.5
We can use The Pythagorean Theorem to find the value of x. The theorem states that , where a and b are the lengths of the legs and c is the length of the hypotenuse.
However, we already know the hypotenuse and one leg. Therefore we can substitute inside the equation to find the missing value.
Hope this helped!