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Max left his house and drove 10 miles north to work. From work, he then drove 24 miles eastern to choose up his daughter from the airport. What is the shortest street Max can to journey to get earlier home?


Explanation:

It is simplest to deal with this using one-of-a-kind triangle formulas. Native the description, we recognize this is a right triangle v legs that 10 and also 24. 10 and 24 space multiples that the distinct triangle through side ratio 5 :12 :13. 

Since us multiplied 5 and also 12 by 2 to acquire 10 and 24, respectively, we compute the diagonal line to be 2 * 13 = 26.

You are watching: A triangle has sides of lengths 10, 24, and 26. is it a right triangle? explain.

Using the Pythagorean Theorem, a2 + b2 = c2, is also an acceptable approach to fixing this problem.


These two triangles (not attracted to scale) are comparable triangles.


Explanation:

These 2 triangles are similar triangles. The triangle ~ above the right is one-third the dimension of the triangle top top the left. We recognize this by comparing the bottom legs of every triangle.

3/9 = 1/3 

Given this, every the other legs that the triangle top top the right will it is in 1/3 the dimension of their equivalent legs ~ above the left.

12 * 1/3 = 418 * 1/3 = 6

Now we know the lengths of the three sides, us simply add them together to receive our answer.

4 + 6 + 3 = 13

An alternate way to carry out this difficulty would be to take it 1/3 the perimeter the the triangle top top the left.

12 + 18 + 9 = 39

1/3 * (39) = 13

Either an approach will permit you to come at the same solution.


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Example concern #24 : appropriate Triangles


Triangle 

*
is identified by the coordinates
*
. What is the perimeter the triangle
*
?


Possible Answers:

*


*



*


Correct answer:


Explanation:

These 3 points kind a ideal triangle on the Cartesian name: coordinates system. The perimeter is consisted of of the size from 

*
; the size from 
*
; and the size of the hypotenuse between
*
.

The perimeter is

*
.


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Example question #25 : ideal Triangles


Quantity A: The perimeter that a appropriate triangle with two brief sides that 10 and 24.

Quantity B: The area the a appropriate triangle through two brief sides of 10 and also 12.


Possible Answers:

The two quantities are equal.


The relationship cannot be determined from the information given.


Quantity A is greater.


Quantity B is greater.


Correct answer:

The two amounts are equal.


Explanation:

In stimulate to uncover the perimeter of the right triangle in amount A, we must uncover the length of the hypotenuse. We know that through the Pythagorean theorem, the hypotenuse is same to the square source of (102 + 242) = 100 + 576 = 676. The square source of 676 is 26, therefore the perimeter the the ideal triangle is 10 + 24 + 26 = 60.

The area the the ideal triangle is calculated v b * h / 2, through the base and height same to the two short sides the the right triangle. 10 * 12 / 2 = 120 / 2 = 60.

Thus, the two quantities are equal.


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Example concern #26 : appropriate Triangles


Quantity A:

The perimeter of a right triangle through a hypotenuse that

*

Quantity B: 

*
.


Possible Answers:

Quantity A is greater.


The two amounts are equal. 


Quantity B is greater.


The relationship cannot be identified from the information given.


Correct answer:

The partnership cannot be figured out from the information given.

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Explanation:

The very first step in quantitative comparison troubles is come make sure they can actually it is in solved. Quantity B is simply a number. Quantity A is a ideal triangle, where we"re offered the hypotenuse, the triangle"s classification/an angle measure, and also asked to find a perimeter. And also we cannot.

How perform we recognize that?

But, host on a second. Draw an additional triangle, additionally with a best angle and also a hypotenus of 13, but this time, make the triangle isosceles. It"s possible, right? You have met every the conditions Quantity A gives you in this triangle, as well, however it will have actually a various perimeter.

Therefore, the information in quantity A is not sufficient information to determine what the answer is, and that"s the price you should put.