The two shorter sides of a right triangle differ by 7 cm. If the area is 30 cm^2, find the hypotenuse.

Question

solve and type an equation

Answer 1

x(x + 7)/2 = 30

x² + 7x = 60

x² + 7x - 60 = 0

(x + 12)(x - 5) = 0

 

x + 12 = 0

x = -12

Because we don't measure in negative units, this answer is out.

 

x - 5 = 0

x = 5

 

5² + 12² = c²

c² = 169

c = 13 cm

 

Answer 2

x = the shorter side of the triangle

 

x + 7 = the longer side

 

area of a triangle = h·b/2

 

(x)(x+7)/2 = 30

 

x² +7x = 60

 

x² + 7x - 60 = 0

 

(x+12)(x-5) = 0

 

x can't be -12 so x=5

 

One side is 5 and the other side is 7 more which is 12

 

Hypotenuse² = 5² + 12² = 25 + 144 = 169

 

hypotenuse = 13