All categories

2 years ago

The two shorter sides of an obtuse triangle measure 15 inch and 3 ft describe the length of the longest side

Mathematics

1 answer:

Nat2105 [25]2 years ago

3 0

Answer:

The length of the longest side are all real numbers greater than 39 inches and less than 51 inches

Step-by-step explanation:

we know that

In an obtuse triangle

$c^{2} >a^{2}+b^{2}$

where

c is the length of the longest side

a and b are the two shorter sides

Convert the dimensions in inches

$1\ ft=12\ in$

$3\ ft=3*12=36\ in$

substitute the values

$c^{2} >15^{2}+36^{2}$

$c^{2} >1,521$

$c >39 in$

Applying the triangle inequality Theorem

1) $15+36 >c$

$c$

2) $c+15 >36$

$c>21 in$

therefore

The length of the longest side belong to the interval $(39,51)$

All real numbers greater than 39 inches and less than 51 inches

You might be interested in

What is the probability of rolling a number greater than or equal to 9 with the sum of two dice, given that at least one of the

olga55 [171]

Conditional probablility P(A/B) = P(A and B) / P(B). Here, A is sum of two dice being greater than or equal to 9 and B is at least one of the dice showing 6. Number of ways two dice faces can sum up to 9 = (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6) = 10 ways. Number of ways that at least one of the dice must show 6 = (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6), (6, 5), (6, 4), (6, 3), (6, 2), (6, 1) = 11 ways. Number of ways of rolling a number greater than or equal to 9 and at least one of the dice showing 6 = (3, 6), (4, 6), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6) = 7 ways. Probability of rolling a number greater than or equal to 9 given that at least one of the dice must show a 6 = 7 / 11

6 0

2 years ago

Bridgette made a graph of her neighborhood on a coordinate grid. The points A(-2, 3), B(-2, -2), C(2, -2), and D(2, 3) represent

vodka [1.7K]

Answer:

$\boxed{\text{18 blocks}}$

Step-by-step explanation:

Distance travelled on graph = AB + BC + CD + DA

AB = CD = (3 +2) = 5

BC = AD = 2 –(-2) = 4

Distance on graph = 2 × 5 + 2 × 4 = 10 + 8 = 18 spaces = 18 blocks

Bridgette jogs $\boxed{\textbf{18 blocks}}$ each day.

8 0

3 years ago

A cylindrical water bottle has a diameter of 5 in. and a height of 9 in. What is the capacity of the water bottle in cubic inche

VikaD [51]

The answer will be 388.6 because you will use the formula V=pi.r^2.h.
pi we know is 3.14 we also know that radius is half the diameter so half of 5 is 2.5 and the height is 9 so here is what we have so far. V=3.14x2.5^2x9.
2.5x2.5=13.75 13.75x3.14=43.175 43.175x9=388.575 and if we round that it will be 388.6 so your answer is 388.6

3 0

3 years ago

A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line

anzhelika [568]

Answer:

570 m³

Step-by-step explanation:

The volume of water is the product of flow rate of water and the time taken. We are to get the volume of water used between 6 am and 9 am, that is for 3 hours (9 - 6).

We are given the flow rate at 6 am and the flow rate at 9 am, but this flow rate changes between 6 am and 9 am. To get the estimate of the water used, Let us assume that it flows at the same flow rate as it was at 6 am throughout, hence:

$V_L= 100 m^3/h * 3h=300\ m^3$