the ratio of the height of a triangle to its base is 2:3. If the height of the triangle is 18cm, what is the length of the base

Mathematics

1 answer:

Mice21 [21]3 years ago

7 0

Answer:

27 cm

Step-by-step explanation:

Hi there!

Let <em>b</em> be equal to the length of the base.

Form a proportion:

$\displaystyle \frac{2}{3} =\frac{18}{b}$

Cross multiply:

$3*18=2b\\54=2b\\b=27$

Therefore, the length of the base is 27 cm.

I hope this helps!

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Read 2 more answers

Jason and Britton are driving to St. George. Jason got a 20 mile head start and drove an

harina [27]

Answer:

2 hours, 150 miles

Step-by-step explanation:

The relation between time, speed, and distance can be used to solve this problem. It can work well to consider just the distance between the drivers, and the speed at which that is changing.

<h3>Separation distance</h3>

Jason got a head start of 20 miles, so that is the initial separation between the two drivers.

<h3>Closure speed</h3>

Jason is driving 10 mph faster than Britton, so is closing the initial separation gap at that rate.

<h3>Closure time</h3>

The relevant relation is ...

time = distance/speed

Then the time it takes to reduce the separation distance to zero is ...

closure time = separation distance / closure speed = 20 mi / (10 mi/h)

closure time = 2 h

Britton will catch up to Jason after 2 hours. In that time, Britton will have driven (2 h)(75 mi/h) = 150 miles.

<em>Additional comment</em>

The attached graph shows the distance driven as a function of time from when Britton started. The distances will be equal after 2 hours, meaning the drivers are in the same place, 150 miles from their starting spot.