[ceb0621]

How do you calculate the length of the sides of an isoceles triangle when given a perimeter of 24 and altitude of 9?

[ROLCAM]

USING EXCEL!
Feed in the necessary data and you get the answer.

When given a perimeter of 24 and altitude of 9?
The length of the sides of an isoceles triangle
are:-

1) 9.37
2) 9.37
3) 5.26
Total = 24

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One needs more decimal places for the accuracy of the proof.

[sarnian]

Hello ceb0621

As this is math homework, let's do math instead of using calculators or excel!
You have to understand what you do, and how you do that! You need that at your next exam!

We have an isoceles triangle with a perimeter of 24 and altitude of 9.
A triangle is isoceles if it has 2 sides of equal length (2 angles are equal).
We know the height of the triangle (9) and the perimeter (24)

So if we drop a median from the top , we get the following drawing for the left hand section ONLY (LINK)

The total perimeter is given (2c + 2b =24), so c + b = 12, or c = 12 - b (*)

We know that a = 9, and that the angle of C has to be 90 degrees.
We also know that a² + b² = c².
a² = c² - b². As a = 9 :
c² - b² = 81
c² = b² + 81
c = root (b² + 81) and c = 12 - b (see *)
So root (b² + 81) = 12 - b
12 - b = root (b² + 81)
(12 - b)² = b² + 81
144 - 24b + b² = b² + 81
144 - 24b = 81
-24b = 81 - 144
24b = 144 - 81 = 63
b = 2.625
So c = 12 - 2.625 = 9.375

The CORRECT values of the sides of the isoceles triangle are : 9.375 , 9.375 , and 2b = 5.25