## Elementary Geometry for College Students (7th Edition)

Given The perimeter of a right triangle is 12 m. If the hypotenuse has a length of 5 m, We need to find the lengths of the two legs. Lets assume that the right triangle legs are a and b Perimeter = a+b+ hypotenus 12 = a+b + 5 a+b = 7m By pythagoras theorem $hypotenus^{2}$ =$a^{2}$ + $b^{2}$ $5^{2}$ = $(b-7)^{2}$ + $b^{2}$ 25 = $b^{2}$ + 49 -14b + $b^{2}$ 25 = 2$b^{2}$ +49 -14b 2$b^{2}$ +24 - 14b = 0 $b^{2}$ - 7b + 12= 0 $b^{2}$ -3b -4b +12 = 0 b(b-3) - 4(b-3) = 0 (b-4)(b-3) = 0 (b-4) =0, (b-3) = 0 So, b =4,3 Now use the value of b in a+b = 7m a+4=7 a =3 or a+3=7 a=4 So legs of the right triangle be(3,4)(4,3)