Question

Second degree equation
The peimeter of a right angled mangle is 36 cm
the length of hypotenuse is 15 cm. find the length
of its other side?​

Answer 1

Step-by-step explanation:

This is the way you are expected to do it.

First subtract 36 - 15 = 21. The two legs of the triangle add up to 21.

Call one of them x and the other 21-x.

Use the Pythagorean Theorem:

15^2 = x^2 + (21-x)^2

225 = x^2 + 441 - 42x + x^2

225 = 2(x^2) - 42x + 441

0 = 2(x^2) - 42x + 216, Factor a 2 out on the right and divide both sides by 2.

0 = x^2 - 21x + 108, Factor the quadratic.

0 = (x - 9)(x - 12)

x - 9 = 0 or x - 12 = 0

x = 9 or 12. So these are the lengths of the two legs.

There is a shorter way if you are acquainted with the 3–4–5 right triangle. It is a right triangle because 9 + 16 = 25. Its multiples are also right triangles because they are similar to the 3–4–5.

Multiply by 2 and you get 6–8–10.

Multiply by 3 and you get 9–12–15. This is the triangle you arrived at.

These are some of the favorite triangles you find in textbooks, because they are some of the few that have nice, small whole numbers for sides.

Whenever I see 15 or 10 or 5 on a hypotenuse, the alarm goes off, and I check to see if it is one of those. When I added 9+12+15, I got 36. That saved me a ton of work. This is great when you are pressed for time and just need a fast answer, but it won’t satisfy a teacher who is looking for your work, and it won’t help you become proficient at algebra. Also, it won’t work if it doesn’t turn out to be one of those nice, familiar right triangles. For future reference, another right triangle is 5–12–13. Check it out.