(a) The area of triangle F is 4 times the area of triangle G.
(b) The area of triangle B is 1/4 times the area of triangle G.
(c) The area of triangle F is 16 times the area of triangle B.
(d) The area of triangle H is 1/9 times the area of triangle F.
(e) The area of triangle H is 4/9 times the area of triangle G.
(f) The area of triangle B is 9/16 times the area of triangle H.
(a) Triangle G and Triangle F
Consider triangle F,
The height of the triangle is 8.
The base of the triangle is 6.
The hypotenuse of the triangle is 10.
Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.
Consider triangle G,
The height of the triangle is 4.
The base of the triangle is 3.
The hypotenuse of the triangle is 5.
Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units.
Therefore,
Area of ΔF = 4 × Area of ΔG
(b) Triangle G and Triangle B
Consider triangle G,
The area of the triangle is:
Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units.
Consider triangle B,
The height of the triangle is 2.
The base of the triangle is 3/2.
The hypotenuse of the triangle is 5/2.
Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units.
Now, 4 × 3/2 = 6
Therefore,
Area of ΔG = 4 × Area of ΔB
Area of ΔB = 1/4 × Area of ΔG
(c) Triangle B and Triangle F
Consider triangle B,
Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units.
Consider triangle F,
Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.
Now, 16 × 3/2 = 24
Therefore,
Area of ΔF = 16 × Area of ΔB
(d) Triangle F and Triangle H
Consider triangle F,
Area of ΔF = ( 1/2 ) × b × h = ( 1/2 ) × 6 × 8 = 24 square units.
Consider triangle H,
The height of the triangle is 8/3.
The base of the triangle is 2.
The hypotenuse of the triangle is 10/3.
Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units.
Now, 9 × 8/3 = 24
Therefore,
Area of ΔF = 9 × Area of ΔH
Area of ΔH = 1/9 × Area of ΔF
(e) Triangle G and Triangle H
Consider triangle G,
Area of ΔG = ( 1/2 ) × b × h = ( 1/2 ) × 3 × 4 = 6 square units
Consider triangle H,
Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units.
Now,
9/4 × 8/3 = 6
Therefore,
Area of ΔG = 9/4 × Area of ΔH
Area of ΔH = 4/9 × Area of ΔG
(f) Triangle H and Triangle B
Consider triangle H,
Area of ΔH = ( 1/2 ) × b × h = ( 1/2 ) × 2 × 8/3 = 8/3 square units
Consider triangle B,
Area of ΔB = ( 1/2 ) × b × h = ( 1/2 ) × 3/2 × 2 = 3/2 square units
Now,
16/9 × 3/2 = 8/3
Therefore,
Area of ΔH = 16/9 × Area of ΔB
Area of ΔB = 9/16 × Area of ΔH
Learn more about area here:
brainly.com/question/23945265
#SPJ1
