The perimeter of a right angle triangle is 30cms and it's hypotenuse is 13cms find the length of the other two sides
Answers!
Hi Balaji,
Perimeter = 30 cm
Hypotenuse = 13 cm
Now,
Perimeter = Base + Height + Hypotenuse
30 = Base + Height + 13
30 - 13 = Base + Height
Base + Height = 17
Base = (17 - Height)
Now, in a right angled Triangle
(Hypotenuse)2 = (Base)2 + (Height)2
(13)2 = (17 - Height)2 + (Height)2
(13)2 = (17 - H)2 + (H)2
169 = 172 + H2 - 2(17)H + H2
169 = 2H2 - 34H + 289
0 = 2H2 - 34H + 289 - 169
2H2 - 34H + 120 = 0
2(H2 - 17H + 60) = 0
H2 - 17H + 60 = 0
H2 - 12H - 5H + 60 = 0
H(H - 12) - 5(H - 12) = 0
(H - 5) (H - 12) = 0
So, H = 5, 12
If H = 5, Base = 17 - H = 17 - 5 = 12
If H = 12, Base = 17 - H = 17 - 12 = 5
Thus, the other two sides are 12 and 5
Comment
There are 16 cricket players ina club 5 are batsmen 4 are bowlers and rest are all-rounders in how many ways a team of 11 will be selected so has to contain 3 batsman 2 bowlers and the remaining all rounders
Answer the question...
Hi Balaji,
Perimeter = 30 cm
Hypotenuse = 13 cm
Now,
Perimeter = Base + Height + Hypotenuse
30 = Base + Height + 13
30 - 13 = Base + Height
Base + Height = 17
Base = (17 - Height)
Now, in a right angled Triangle
(Hypotenuse)2 = (Base)2 + (Height)2
(13)2 = (17 - Height)2 + (Height)2
(13)2 = (17 - H)2 + (H)2
169 = 172 + H2 - 2(17)H + H2
169 = 2H2 - 34H + 289
0 = 2H2 - 34H + 289 - 169
2H2 - 34H + 120 = 0
2(H2 - 17H + 60) = 0
H2 - 17H + 60 = 0
H2 - 12H - 5H + 60 = 0
H(H - 12) - 5(H - 12) = 0
(H - 5) (H - 12) = 0
So, H = 5, 12
If H = 5, Base = 17 - H = 17 - 5 = 12
If H = 12, Base = 17 - H = 17 - 12 = 5
Thus, the other two sides are 12 and 5
Comment
There are 16 cricket players ina club 5 are batsmen 4 are bowlers and rest are all-rounders in how many ways a team of 11 will be selected so has to contain 3 batsman 2 bowlers and the remaining all rounders