Triangles — Practice

Question 1

Find the hypotenuse of a right triangle with legs 5 cm and 12 cm.

Accepted Answer

✦ Answer: c² = 5² + 12² = 25 + 144 = 169. c = 13 cm. (Pythagorean triple 5-12-13.)

Question 2

Two similar triangles have sides in ratio 3:4. Find the ratio of their areas.

Accepted Answer

✦ Answer: Area ratio = (3/4)² = 9/16.

Question 3

In △ABC, DE || BC. If AD/DB = 2/3 and AE = 4 cm, find EC.

Accepted Answer

Step 1 — BPT.
  AD/DB = AE/EC (Basic Proportionality Theorem)

Step 2 — Substitute.
  2/3 = 4/EC

Step 3 — Solve.
  EC = 4 × 3 / 2 = 6 cm

✦ Answer: EC = 6 cm.

Question 4

A ladder 17 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the wall.

Accepted Answer

Step 1 — Setup.
  Ladder = hypotenuse = 17 m
  Height up wall = 8 m (one leg)
  Distance from wall = unknown (other leg, let's call x)

Step 2 — Apply Pythagoras.
  17² = 8² + x²
  289 = 64 + x²
  x² = 225
  x = 15 m

Step 3 — Verify.
  Pythagorean triple 8-15-17.

✦ Answer: Distance from wall = 15 m.

Practice — Triangles