Question

If a = 15 and c. 25 what is the length of leg b of a right triangle using the

pythagorean theorem?

Answer 1

Given : In a triangle ABC , a = 15 , c = 25 . Also the triangle is a right angled triangle .

To Find : The value of b using the Pythagoras Theorem.

Solution : The value of side a is 15 , c is 25 and we have to find b . The sides with be Pythagorean Triplet whose smallest member will be 15 . So the third member. will be 20 . And the largest member is 25 .

The Pythagoras Theorem is :

`\boxed{\red{\bf hypontenuse^2=base^2+perpendicular^2}}`

⇒ c² = a² + b² .

⇒ b² = c² - a² .

⇒ b² = ( c + a ) ( c - a ) .

⇒ b² = ( 25 + 15 ) ( 25 - 15 ) .

⇒ b² = 40 × 10.

⇒ b² = 400.

⇒ b² = √400.

⇒ b = 20 .

Hence the value of c is 20 .

Answer 2

b=20

Explanation:

`b ^(2) + {a}^(2) = {c}^(2) \ \\ {b}^(2) = {c}^(2) - {a}^(2) \\ {b}^(2) = {25}^(2) - {15}^(2) = 625 - 225 = 400 \\ b = √(400) = 20`