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:

$A=\dfrac{l_1l_2}{2}$

Substitute:

$\dfrac{l(l+3)}{2}=44$     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 .