Answer:
either h=12, b=5
or h=5, b=12
Explanation:
We'll use a system of equations to solve this. We'll have 2 equations and 2 unknowns. Our 2 unknowns are the 2 other sides, and our 2 equations are as follows:
look for any information given. I see that the area is 30 sq.cm and the perimeter is 30cm. There are our pieces of information.
Our first equation will be the one about how the area is 30 sq.cm (we'll use b for base and h for height:
(1/2)×b×h=30
Our second equation will be the one about how the perimeter is 30cm:
13+b+h=30
These equations both have to be true at the same time, and there are a few techniques for solving a system of equations, but in this case, this way is probably the simplest. We'll get one variable on one side of an equation and then plug it into the other equation using the transitive property.
13+b+h=30
b=30-13-h
b=17-h
now we'll plug in (17-h) for all the b in the first equation:
(1/2)×(17-h)×h=30
17h-h²=60
-h²+17h-60=0
now we'll use quadratic formula (or factor) to find h:
[-17±√(289-240)]/-2
(-17±7)/-2
-24/-2 or -10/-2
12 or 5
h=12
h=5
we'll try both of them in this equation:
13+b+h=30
25+b=30
or 18+b=30
therefore;
either h=12, b=5
or h=5, b=12