Question

An isolates right triangle has a hypotenuse of 6. Find the
length of the leg. Round to the nearest tenth.

Answer 1

Check the picture below.

Answer 2

• Hypotenuse of the ∆ = 6
• Given that it is an isosceles right triangle.
• So, its opposite sides will be equal.
• Therefore, the height of the ∆ = the length of the leg of the ∆
• Let the length of the leg be x.
• In the right triangle,

${x}^{2} + {x}^{2} = {6}^{2} \: \: \: (by \: \: pythagoras \: \: \: theorem) \\ = > {2x}^{2} = 36 \\ = > {x}^{2} = \frac{36}{2} \\ = > {x}^{2} = 18 \\ = > x = \sqrt{18} \\ = > x = \sqrt{2 \times 3 \times 3} \\ = > x = 3 \sqrt{2 } \\ = > x = 4 .2$

Answer:

Answer:The length of the leg is 4.2 units.

Hope you could get an idea from it.

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