Heron's Formula MCQs

Q1. For a triangle with edges 13 cm, 14 cm and 15 cm, compute the area by Heron's formula and then the two altitudes drawn to the 13 cm edge and to the 15 cm edge; by how much does the first exceed the second?

• A.112/65 cm
• B.168/13 cm
• C.56/5 cm
• D.56/65 cm

Answer: A. 112/65 cm

Q2. For a triangle with edges 10 cm, 24 cm and 26 cm, compute the area by Heron's formula and then the two altitudes drawn to the 10 cm edge and to the 26 cm edge; by how much does the first exceed the second?

• A.192/13 cm
• B.24 cm
• C.120/13 cm
• D.96/13 cm

Answer: A. 192/13 cm

Q3. For a triangle with edges 15 cm, 20 cm and 25 cm, compute the area by Heron's formula and then the two altitudes drawn to the 15 cm edge and to the 25 cm edge; by how much does the first exceed the second?

• A.8 cm
• B.20 cm
• C.12 cm
• D.4 cm

Answer: A. 8 cm

We are told that 15 cm, 20 cm, 25 cm (math, chapter 'Heron's Formula'). What we must find: compute the area by Heron's formula and then the two altitudes drawn to the 15 cm edge and to the 25 cm edge; by how much does the first ex. This is a classic application of s = (15+20+25)/2 = 30. Crunching it out: s = (15+20+25)/2 = 30 → Heron area = 150 → altitude to 15 = 2×.150/15 = 20 → to 25 = 2×.150/25 = 12. So the correct choice is A) 8 cm. As for the others, option B) '20 cm' fails since Give the DIFFERENCE of the two altitudes; option C) '12 cm' is incorrect: That is the second altitude, not the difference.