math...question in details?

Question

in a right triangle, the measures of the legs are 7 and x-1, and the measure of the hypotenuse is x. Find the value of x.

Answer 1

Use Pythagorean's Theorem.

"The sum of the square of the legs of a right triangle is equal to the square of the hypotenus."

In otherwords, a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenus.

7² + (x - 1)² = x²

FOIL

49 + x² - x + 1 = x²

subtract x² from each side and combine 49+1

50 - x = 0

x = 50


There you go!

Answer 2

Pythagorean theorem is

a² + b² = c²

where c is the hypotenuse

7² + (x - 1)² = x²

49 + x² - 2x + 1 = x²

Subtract x² from both sides and combine terms.

49 - 2x + 1 = 0

50 - 2x = 0

2x = 50

x = 25 (hypotenuse)

x - 1 = 24 one of the legs

So the triangle is a 7, 24, 25 right triangle
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Answer 3

a²+b²=c²

Substituting what we know…
7² + (x-1)² = x²

Doing the multiplying…
49 + x² - 2x +1 = x²

Dong some arithmetic…
x² - 2x + 50 = x²

Adding –x² +2x to both sides…
50 = 2x

Multiplying both sides by ½
25=x

If you wish, you can add this to the list of triangles like 3-4-5, 5-12-13, and now 7-24-25

Answer 4

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49 +x^2 -2x +1 = x^2
50 =2x
x = 25