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2 years ago

6

a drawing of a room has a scale of 1 inch = 4 feet. if the actual dimensions of the room are 14 feet by 16 feet. what are the di

mesnsions of the room o on the drawing

1 answer:

disa [49]2 years ago

3 0

Answer:

3.5 inches by 4 inches

Step-by-step explanation:

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What is the constant of proportionality in the equation StartFraction x over y EndFraction = StartFraction 2 over 9 EndFraction?

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2 years ago

At a certain time of the day, a tree that is x meters tall casts a shadow that is x-49 meters long. If the distance from the top

nikklg [1K]

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of $x-49$ meters and the distance from the top of the tree to the end of the shadow is $x+1$ meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

$x^{2}+(x-49)^{2}=(x+1)^{2}$

Expanding, we get,

$2 x^{2}-98 x+2401=x^{2}+2 x+1$

$2 x^{2}-98 x+2400=x^{2}+2 x$

$2 x^{2}-100 x+2400=x^{2}$

$x^{2}-100 x+2400=0$

Solving the equation using the quadratic formula $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ , we get,

$x=\frac{-(-100)\pm\sqrt{(-100)^{2}-4 \cdot 1 \cdot 2400}}{2 \cdot 1}$

Simplifying, we have,

$x=\frac{100\pm\sqrt{10000-9600}}{2}$

$x=\frac{100\pm\sqrt{400}}{2}$

$x=\frac{100\pm{20}}{2}$

Thus,

$x=\frac{100+20}{2} \\x=\frac{120}{2} \\x=60$ and $x=\frac{100-20}{2} \\x=\frac{80}{2} \\x=40$

where the value $x=40$ is not possible because substituting the value $x=40$ in $x-49$ results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

7 0

2 years ago