the shorter leg of a right triangle is 7 centimeters less than the other leg. find the length of the two legs if the hypotenuse is 35 centimeters

Question

the shorter leg of a right triangle is 7 centimeters less than the other leg. find the length of the two legs if the hypotenuse is 35 centimeters

Answer 1

Caitlin, first of all set up each variable for the two side of the triangle.

 

Let x= length of one side of the triangle

and x-7= the length of the other side.

 

Utilize the Pythagorean theorem to set up the equation to solve for x.

 

x^2+(x-7)^2=35^2

x^2+x^2-14x+49=1225

2x^2-14x+49=1225

             -1225  -1225

 

2x^2-14x-1176=0

 

Use the quadratic formula.

 

x=(14±√(14^2-4(2)(-1176)))/(2*2) 

 

x≠-21  x=28 centimeters

 

The shorter leg is 28-7=21 centimeters 

Answer 2

Let's start by calling the length of the unknown leg x.  Then the length of the other leg is x-7.  So by the Pythagorean Theorem, we get x^2+(x-7)^2=35^2.  FOILing everything out and combining like terms, we get 2x^2-14x-1176=0.  We can use the Quadratic formula to solve this and get a value for x, which will give us the length of the legs.  I'll leave that step to you.