The length of shorter leg in millimeter

Question

One leg of a right triangle is 1 millimeter longer than the shorter leg and the hypotension is 2 millimeters longer than the shorter leg. Find the lengths of the sides of the triangle

Answer 1

The word is hypotenuse not hypotension. This is the longest side of a right angled triangle (not a right triangle). Unfortunately this does not allow me draw a diagram below to visualize the problem but drawings always help. Let the short side be x, this is the adjacent. Then we know the opposite side is 1 + x and the hypotenuse is 2 + x

 

Now we use Pythagorean theorem

 

(2+x)² = (1+x)² + x

(2+x)(2+x) =(1+x)(1+x) +x

 

Then we expand

 

4 +2x +2x + x² = 1 + x +x + x²+ x²

 

x² +4x + 4 = 2x² + 2x + 1

 

Collect like terms

 

-x² + 4x +4 = 2x + 1

-x² + 2x + 4 = 1

-x² + 2x + 3 = 0

x² - 2x -3 = 0

 

Now we have a quadratic equation

 

x² - 2x - 3 = 0

 

what 2 numbers cam we multiply to get -3 and add to get -2?

 

x = -3 and x = 1

 

in this case the length equals 1 because this is the positive number.

 

SO the length of the adjacent is 1 millimeter, the opposite is 2 millimeters and the hypotenuse is 3 millimeters.