Question

The length of the hypotenuse of ΔLMN given below is 8.7 cm. If the length of its base is 6 cm, find the height of the triangle.

Answer 1

Answer:

6.3

Step-by-step explanation:

1. Write an equation. Use the Pythagorean Theorum, which is A²+B²=C², where A and B are the two sides that unite to make a right triangle and C is the hypotenuse.
2. Substitute values. We know that C, the hypotenuse is 8.7 cm. Let A be 6. 6²+B²=8.7²
3. Simplify. Do all the multiplication you can. 36+B²=75.69
4. Isolate B. First, subtract 36 from both sides. B²=39.69
5. Finish isolating B. Square root both sides. √B²=√39.69
6. Simplify. A √ and ² cancel eachother out. The square root of 39.69 is 6.3. B=6.3 This means that side B is 6.3 cm long.
7. Check to see if your answer is correct by replacing the B in the original equation with 6.3 6²+6.3²=8.7² becomes 36+39.69=75.69, which is further simplified into 75.69=75.69.

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