Maths prob!!!algebra!!!?

Question

............/~~\.........
.........../~~~\........
...40>/~~~~\<40
........./__x__\......
......../~~~~~~\.....
60>/~~~~~~~\<60
...../~~~~~~~~\...
..../~~~~~~~~~\..
______ Y_____
Isosolese triangle
60m is how long the side is
40m is how long the side is
therefore one side equals 100 metres
i need to know what size is x and y.

the only thing that was given to me was x+y=80, which obviously means the x side and the y side both add to equal 80

how can i find what the number is???
(the answers is said to be a decimal)

please show all your working out and all ideas!!!

Answer 1

You have one equation for x and y. You need a second to find a solution -- as a rule of thumb you need as many equations as you have variables or unknowns.

Putting x and y on triangles that share a vertex is a hint to where you can find the second equation. Given the shared angle (opposite the bases x and y) is the same, and the sides on either side of that angle are in the same ratio (40/(40+60) on the left = 40/(40+60) on the right), you can prove that the two triangles are similar.

Knowing that you have similar triangles, you know that the ratio of each corresponding pair of sides is the same. So you can equate the ratio of the left or right-hand sides and the ratio of the bases x and y:

40/(40+60) = x/y

Simplifying that:

40/(40+60) = x/y
40/100 = x/y
2/5 = x/y
5x = 2y

Now you have a second equation, and can proceed to solve for x and y.

You also know that x + y = 80:

x + y = 80
x = 80 - y

Use that to substitute into the previous equation:

5x = 2y
5(80 - y) = 2y
400 - 5y = 2y
400 = 7y
y = 400/7 = 57 + 1/7 = about 57.14

Now that you know y, use the same equation to find x:

5x = 2y
5x = 2*(400/7)
x = (800/7)/5
x = 160/7 = 22 + 6/7 = about 22.86

You can check your answer, if you want, two ways. First, is the sum of x and y 80?

x + y =? 80
(22 + 6/7) + (57 + 1/7) =? 80
79 + 7/7 =? 80
79 + 1 =? 80
80 = 80

Second, is the ratio of x to y also 2 to 5?

x/y =? 2/5
(160/7) / (400/7) =? 2/5
160/400 =? 2/5
(160/80)/(400/80) =? 2/5?
2/5 = 2/5

By "the answer is said to be a decimal," that probably means that they want the answer in decimal form. I gave those values above, but when checking the answer it's best to use the not-rounded-off version. Otherwise, you'd find that the ratio of 22.86 to 57.14 isn't exactly 2 to 5 (2/5 = 0.4 exactly, but 22.86/57.14 = 0.40007) due to the rounded-off values not being perfectly accurate.

Answer 2

Eh... neither... yet i assume i'm going to go with English. I used to love English extra yet extreme college made it uninteresting. -_- yet I nevertheless love writing as a pastime (and hate math, even although i'm no longer undesirable at it) so i'm going to easily say English.