![ErrorNameTaken505](/avatars/23201.jpg)
ErrorNameTaken505
29.07.2021 •
Mathematics
A Triangle with an area of 24 square feet has a side of length 10 feet. If all 3 sides are even integers, what is the perimeter of the triangle?
Solved
Show answers
More tips
- S Style and Beauty How Are Eyelash Extensions Applied? All Your Questions Answered...
- F Family and Home Tender Care for Your Parquet: Is it Possible to Clean Parquet?...
- S Society and Politics Is It Fact or Fiction? Let s Talk About Anton Chekhov s Pseudonym...
- S Sport Playing Bowling: Rules and Advice for Novices...
- C Computers and Internet How to Properly Repartition a Hard Drive?...
- A Auto and Moto What Is the Cost of Customs Clearance for a Car in Russia?...
- L Leisure and Entertainment Should You Buy a Ceramic Knife?...
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
- F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
Answers on questions: Mathematics
- M Mathematics A bag of peanuts could be divided among 8 children, 9 children, or 10 children with each getting the same number, and with 2 peanuts left over in each case. What is the smallest number...
- M Mathematics Need help plz ! write equations for the verticals and horizontal lines passing through the point (5,8) vertical line : horizontal line :...
- M Mathematics Help please ..............
- M Mathematics Find the slope of the line that is a parallel and be perpendicular to the line through the Parallel and perpendicular to the line through the pair of points (-3,-9) and (0,0)...
- M Mathematics Please explain to me thanks...
- M Mathematics Liz deposited money into an account in which interest is compounded quarterly at a rate of 3.2%. How much did she deposit if the total amount in her account after 5 years was $4837.65,...
- M Mathematics Which exponential function is represented by the table?...
- M Mathematics Find the area of this triangle. Round to the nearest tenth....
- M Mathematics How do you get an out put from (x-7)/3...
- M Mathematics Arrange the functions in ascending order, starting with the function that eventrually has the least value and ending with the function that eventually has the greatest value 5 x+3...
Ответ:
24 ft
Step-by-step explanation:
so, we don't know anything else about the triangle ?
ok, let's see.
the area of a triangle is (a side length) × (the height from that side to the opposite corner) / 2
At = 24 = side × height / 2
48 = side × height = 10 × height
height = 48/10 = 4.8 = 24/5
let's say that the height on our known side splits this side into 2 parts, p and q (p+q = 10).
we can calculate the triangle side on the right hand side of our know side by calling it a and using Pythagoras :
a² = height² + q² = (4.8)² + q² = 23.04 + q²
as all sides have to be even integers, a² has to be an even square number larger than 23.04.
and because p+q = 10, we know q must be smaller than 10, and therefore q² smaller than 100.
the only candidates for a² are therefore 36 and 64 (6² and 8²).
in a similar way this applies to the left hand triangle side b tool.
b² = height² + p² = 23.04 + p²
with the same restrictions and possible solutions as a².
we have the possibilities that a = b = 6 or 8, or a = 6 and b = 8 (or vice versa).
let's rule out a=b :
a=b wound also mean p=q=5
then
a² = 23.04 + 5² = 23.04 + 25 = 48.04, which is not an even square integer. therefore, this assumption is wrong.
so, the only possible solution is a = 6 and b = 8 (or vice versa, but it did not matter which is which, as we only need the perimeter, which would be the same either way).
proof :
36 = 23.04 + 12.96 = 23.04 + q²
=> q = 3.6 ft
64 = 23.04 + 40.96 = 23.04 + p²
=> p = 6.4 ft
p+q = 3.6 + 6.4 = 10 ft
perfect, it fits, this is the correct solution
so, the perimeter of the triangle is
10 + 6 + 8 = 24 ft
Ответ:
Try taking a screen shot as this is indecipherable.
Step-by-step explanation: