Mathematics

Mathematics

Problem

Find the value of xx so that 11 cm, 60 cm and xx cm can be the sides of a right triangle. a) 5959 b) 6565 c) 6161 d) 6262
Intuitive explanation

The key insight is the Pythagorean theorem: in any right triangle, the sum of the squares of the two shorter sides equals the square of the longest side. Here, you need to figure out which of your three lengths is the hypotenuse (the longest side opposite the right angle), then apply a2+b2=c2a^2 + b^2 = c^2 to solve for xx. Since 60 cm is already quite long, consider whether it's the hypotenuse or one of the legs.

Intuitive explanation

The key insight is the Pythagorean theorem: in any right triangle, the sum of the squares of the two shorter sides equals the square of the longest side. Here, you need to figure out which of your three lengths is the hypotenuse (the longest side opposite the right angle), then apply a2+b2=c2a^2 + b^2 = c^2 to solve for xx. Since 60 cm is already quite long, consider whether it's the hypotenuse or one of the legs.

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