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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.

2007-06-09 09:11:40 · 4 answers · asked by Anonymous in Science & Mathematics Mathematics

4 answers

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!

2007-06-09 09:17:53 · answer #1 · answered by Boozer 4 · 0 0

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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2007-06-09 16:21:01 · answer #2 · answered by Robert L 7 · 0 0

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

2007-06-09 16:24:13 · answer #3 · answered by gugliamo00 7 · 0 0

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

2007-06-09 16:20:35 · answer #4 · answered by derek1079 5 · 0 0

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