Question

The area of a right triangle is 44m2. find the lengths of its legs if one of the legs is 3m longer

Answer 1

`A=44\ m^2\\\\l,\ l+3-the\ lengths\ of\ legs`

The formula of an area of a right trinagle:

`A=(l_1l_2)/(2)`

Substitute:

`(l(l+3))/(2)=44` multiply both sides by 2

`l(l+3)=88` use distributive property

`l^2+3l=88` subtract 88 from both sides

`l^2+3l-88=0`

`l^2+11l-8l-88=0`

`l(l+11)-8(l+11)=0`

`(l+11)(l-8)=0\iff l+11=0\ \vee\ l-8=0\\\\l=-11<0\ \vee\ l=8`

`l=8\\l+3=8+3=11`

Answer: 8 m and 11 m .