The hypotenuse of an isosceles right triangle is 10. What are its other two sidelengths? [Hint: Find the area of the square composed of two such right triangles.]
The other two sides each have length 5 7.07 units.
Explanation
The chapter establishes that for an isosceles right triangle with equal sides 'a' and hypotenuse 'c', the relation c² = 2a² holds. Given c = 10, we have 100 = 2a², so a² = 50 and a = = 5. The hint suggests using the area relationship: a square of side 'a' is made of two such triangles, and the square on the hypotenuse has twice that area.
Solution Steps
Step 1: For an isosceles right triangle, c² = 2a² where c is the hypotenuse and a is the length of equal sides.
Step 2: Given c = 10, substitute: 10² = 2a²
Step 3: Simplify: 100 = 2a²
Step 4: Solve for a²: a² = 100/2 = 50
Step 5: Find a: a = = \sqrt{$$25 \times 2$$} = 5 7.07 units