Answer:
see explanation
Step-by-step explanation:
(1)
given 3 sides of a triangle , a , b , c
with c being the longest side
• If a² + b² = c² ⇒ right triangle
given the 3 sides 15 , 20 and 25
let a = 15 , b = 20 and c = 25 , then
a² + b² = 15² + 20² = 225 + 400 = 625
c² = 25² = 625
Since a² + b² = c² , then the 3 sides form a right triangle
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(2)
Using Pythagoras' identity in the right triangle
• a² + b² = c² ( c is the hypotenuse and a, b the legs
let a = 15 , b = 8 and c = walkway , then
15² + 8² = c²
225 + 64 = w²
289 = w² ( take square root of both sides )
[tex]\sqrt{289}[/tex] = [tex]\sqrt{w^2}[/tex] , that is
w = 17
The walkway is 17 feet long
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(3)
Using Pythagoras' identity in the right triangle
let a = x , b = 7 and c = 18.4 , then
x² + 7² = 18.4²
x² + 49 = 338.56 ( subtract 49 from both sides )
x² = 289.56 ( take square root of both sides )
[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{289.56}[/tex]
x ≈ 17 cm ( to the nearest cm ) , that is option 2
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(4)
The diagonal divides the rectangle into 2 right triangles
Using Pythagoras' identity in the right triangle with the diagonal the hypotenuse
let a = 48 , b = 40 and c = diagonal, then
c² = 48² + 40² = 2304 + 1600 = 3904 ( take square root of both sides )
[tex]\sqrt{c^2}[/tex] = [tex]\sqrt{3904}[/tex]
c ≈ 62 in ( to the nearest inch ) , that is option 2
