write the Pythagorean triplet whose one member is 14
Answers
In a Pythagorean Triplet we have three values. The base, length and the hypotenuse. It is only used for right angled triangles. Hypotenuse is the largest side.
For finding the base, height and hypotenuse the formulas are given below.
- Base ⇒ 2m
- Height ⇒ m² - 1
- Hypotenuse ⇒ m² + 1
Let's find whether '14' is the base, height or hypotenuse.
Base
⇒ 2m
⇒ 2m = 14
⇒ m = 14 ÷ 2
⇒ m = 7
∴ 14 could be the base.
Height
⇒ m² - 1
⇒ m² - 1 = 14
⇒ m² = 14 + 1
⇒ m² = 15
⇒ m = √15
∴ 14 can't be the height since it doesn't give the value of 'm' in whole value.
Hypotenuse
⇒ m² + 1
⇒ m² + 1 = 14
⇒ m² = 14 - 1
⇒ m² = 13
∴ 14 can't be the hypotenuse since it doesn't give the value of 'm' in whole value.
∴ 14 is the value of the base.
To find the other values we will use the formula mentioned for each in the start.
m = 7
Base
⇒ 2m
⇒ 2 × 7
⇒ 14
Height
⇒ m² - 1
⇒ 7² - 1
⇒ 49 - 1
⇒ 48
Hypotenuse
⇒ m² + 1
⇒ 7² + 1
⇒ 49 + 1
⇒ 50
∴ The Pythagorean Triplet is 14, 48 and 50.
Let us assume 2 m=14 therefore m=7
Now m²+1=7²+1=49+1=50
And m²−1=7²−1=49−1=48
Test : 14²+48² =196+1304=2500=50²
Hence the triplet is 14,48 and 50.