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3 years ago

A map uses 5cm to mean 24 miles. How many miles matches 13cm?

Mathematics

1 answer:

Doss [256]3 years ago

5 0

Answer:

62.4 miles

Step-by-step explanation:

The way to determine this is to set up a proportion,

5 cm/24 miles = 13 cm/x miles,

and then solve for x by cross multiplying,

5*x = 24*13.

<em>If you don’t understand that step, try writing it out on paper with fractions instead of division signs.</em> Next, solve.

x = 62.4

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3 years ago

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3 years ago

Find the value of x in the isosceles triangle shown below.

guajiro [1.7K]

Answer:

B) $x = \sqrt{60}$

Step-by-step explanation:

1. As you can see from the image, there are two right triangles in the isosceles triangle. The base of each right triangle is 2 (because 4 ÷ 2 = 2), and the hypotenuse is 8.

2. Let's use Pythagorean Theorem to find the height of each right triangle, which will also give us the height of the isosceles triangle: $a^2 + b^2 = c^2$ , where a = height, b = base, and c= hypotenuse.

$a^2 + 2^2 = 8^2$
$a^2 + (2*2) = (8*8)$
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$a^2 + 4 - 4 = 64 - 4$ (Subtract 4 from both sides)
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$\sqrt{a^2} = \sqrt{60}$ (Take square root of both sides
$a = \sqrt{60}$

3. The√(60) is the height of each right triangle, and it's also the height of the isosceles triangle. Therefore, the answer is B) x = √60.

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