word problems

Question

Find the lengths of the legs of a right triangle, if it is known that the sum of the lengths is 23 cm, and the area of the triangle is 60 cm².

Find the lengths of the legs of a right triangle, if it is known that the sum of the lengths is 23 cm, and the area of the triangle is 60 cm².

Answer 1

length of one leg = x

so length of another leg = 23 -x

 

Area = 1/2(one leg * anothr leg)

 

60 =1/2(x*(23-x))

 

120 = 23x -x²

 

x² -23x +120 =0

 

(x-15)(x-8)=0

 

x= 15 and x=8

 

so length of one leg=15

and length of another leg=8