solve for a

Question

a right triangle is provided. hypotenuse is a+1, short leg is a and long leg is 7.we need to solve for a. please help me and explain by steps please!

Answer 1

All right triangles fulfill Pythagorean's Theorem, which states a²+b²=c², or in your case (long leg)²+(short leg)²=(hypotenuse)²

 

• a²+7²=(a+1)²   applying Pythagorean Theorem
• a²+49=a²+2a+1  simplifying
• 49=2a+1   a² terms cancel
• 2a=48    subtract 1
• a=24

Answer 2

a^2+49=(a+1)^2

            =a^2+2a+1

 

2a=48

 

a=24