If each side of a triangle is doubled, how much time will its area be increased?
Answers
A = ½bh
On doubling the sides.
A = ½(2b × 2h) = 2bh
The area increases 4 times the original.
Increase in area = 2 - ½ = 1½ = 3/2
Increase percentage = 3/2÷½×100=300%
Verification
Original triangle, A = ½bh = ½(5 × 6) = 15 cm²
Increased triangle, A = 2bh = 2×5×6 = 60 cm²
By times
Area of Increased triangle = 15 × 4 = 60 cm²
Area of increases triangle by percentage increase = 15×400/100 = 60 cm²
If the sides of a triangle are tribled then by how many times does the area increase?
A = ½bh
A = ½(3b × 3h) = 9/2*bh = 4½bh
The area increases 9 times the original.
Increase in area = 4½ - ½ = 4
Increase percentage = 4÷½×100=800%
Verification
Original triangle, A = ½bh = ½(5 × 6) = 15 cm²
Increased triangle, A = 4½bh = 9/2×5×6 = 135 cm²
By times: 15×9 = 135 cm²
By percentage increase: 15×900/100 = 135 cm²