3 years ago

The diameter of the moon is 2160 miles. A model has a scale of 1in and 150mi. What is the diameter of the model

Mathematics

1 answer:

kaheart [24]3 years ago

3 0

Let x = diameter

x=2160 x (1/150)
x=2160/150
x=14.4

Diameter of the model is 14.4.

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Sidana [21]

Answer:

The correct answer is option 3.

Step-by-step explanation:

Given : ΔPQR, QM is altitude of the triangle

PM = 8

MR = 18

To find = QM

Solution :

PR = 8 + 18 = 26

Let, PQ = x , QR = y, QM = z

Applying Pythagoras Theorem in ΔPQR

$PQ^2+QR^2=PR^2$

$x^2+y^2=(26)^2$ ..[1]

Applying Pythagoras Theorem in ΔPQM

$PM^2+QM^2=PQ^2$

$8^2+z^2=(x)^2$ ..[2]

Applying Pythagoras Theorem in ΔQMR

$MR^2+QM^2=QR^2$

$18^2+z^2=(y)^2$ ..[3]

Putting values of $x^2$ and $y^2$ from [2] and [3 in [1].

$8^2+z^2+18^2+z^2=(26)^2$

$2z^2=(26)^2-(8)^2-(18)^2$

$2z^2=288$

$z^2=144$

z = ±12

z = 12 = QM ( ignoring negative value)

The length of QM is 12.

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Step-by-step explanation:

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