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Grade 11 math
pls help!!!!!

Grade 11 math pls help!!!!!-example-1

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5 votes

Answer:

26cm, 24cm, 10cm

Explanation:

We can use pythagorean theorem to find the equation for the missing side:

a² + b² = c²

n² + missingside² = (2n + 6)²

missingside² = (2n + 6)² - n²

missingside = √[(2n + 6)² - n²]

Now, we know that adding all the sides together should give us 60 (because the perimeter is 60). So, let's write that as an equation:

n + 2n + 6 + √[(2n + 6)² - n²] = 60

now, solve for n:

√[(2n + 6)² - n²] = 60 - n - 2n - 6

√[(2n + 6)² - n²] = 54 - 3n

(2n + 6)² - n² = (54 - 3n)²

4n² + 24n + 36 - n²= 54² - 324n + 9n²

9n² - 3n² - 324n -24n + 54² - 36 = 0

6n² - 348n + 2880 = 0

n² - 58n + 480 = 0

n = 10, n = 48

So have 2 values for n, so we need to see which one works. If we plug both 10 and 48 into our original equation (n + 2n + 6 + √[(2n + 6)² - n²] = 60), we see that only 10 works, not 48. So, n=10.

Now, let's plug n=10 into the equation for each side:

Hypotenuse:

2n + 6 = 2(10) + 6 = 26

Other side:

n = 10

Last side:

√[(2n + 6)² - n²] = √[(2(10) + 6)² - (10)²] = 24

And 26 + 24 + 10 = 60, so we have found the lengths of each side! Let me know if you have other questions about the steps.

User Audrius
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