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vitfil [10]
2 years ago
8

The length of the hypotenuse of a right angled triangle exceeds the length of the base by 2cm and exceeds twice the length of th

e altitude by 1cm.Find the length of each side of the triangle​
Mathematics
1 answer:
insens350 [35]2 years ago
3 0

Answer: a = 8;  b = 15;  c = 17

Step-by-step explanation:

c = b + 2  and c = 2a + 1

b = c − 2 and a =  \frac{c-1}{2}

​

c² = b² + a²  

c^{2} = (c-2)^{2} + \frac{c-1}{2}\\

c^{2}= \frac{4 (c-2)^{2}+(c - 1)^{2}  }{4}

4c^{2}={4 (c^{2} + 4 -4c)+c ^{2}  + 1-2c

4c^{2}={4 c^{2} + 16 -16c)+c ^{2}  + 1-2c

c^{2}-18c+17=0

c(c -17)-1(c-17)=0

​(c -1)(c-17)=0

c = 1 or c = 17

If c = 1 then b = 1 - 2 = -1, that's not possible

So x = 17

b = 17 - 2 = 15

a = \frac{17-1}{2}  = 8

Length sides of the triangle are 17 cm, 15 cm and 8 cm.

I saw some of this on a site but I want to make sure its correct so we're gonna apply the pythagorean theory and see if its correct.

a^{2} + b^{2} = c^{2} \\8^{2} + 15^{2} = 17^{2} \\64 + 225 = 289\\289 = 289\\

This shows that this is correct.

Hope this helped! Again, some of this was from a site, not from me.

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Mark is six years older than his brother Sam. The sum of their ages is 30. Let 'a' be Sam's age.
svlad2 [7]

Answer:

a = 12 years

Step-by-step explanation:

Mark is 6 years older than his brother Sam. Now, we are asked to represent Sam’s age by a. This means that if Sam is a years old, Mark is (a + 6) years old.

The sum of their ages is 30, this means that when we add their ages together, we get the sum of thirty.

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2a = 30 - 6

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a = 24/2

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vesna_86 [32]

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8 0
2 years ago
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Oliga [24]
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