Answer:
the base is 8 cm
Step-by-step explanation:
basically, we need to set up a system of equations.
if we know the area of a triangle is 1/2bh, and that h = b + 5, (because we want them to equal one another in the equation), we can then make two different equations and substitute the h for b.
1/2bh = 52 and h = b+5
subsitute in the (b+5) for the h in the first equation to get
(1/2)(b)(b+5) = 52
multiply both sides by two to get rid of the 1/2
b)(b+5) = 104
now multiply the bs together!
b^2 + 5b = 104
If you know how to factor, we can make this
b^2 +5b -104 and then
(b+13)(b-8) = 0
solve for b to get b = -13, 8, and -13 isn't a real distance, so the only option for b is 8 square centimeters.
Plugging this back into the original equations to get the height (and checking that it is actually right,) we get a height of 13.
When you plug in the 13 and 8 into the area equation, you get
(8)(13)(1/2) = 52
52 = 52
so it works!
lmk if anything is confusing- i know I kind of breezed by the factoring part, but if you have a calculator you can keep dividing 104 by random numbers until you get the right difference if you get kind of lost. The formula
[-b+-sqrt(b^2-4ac)]/2a is another way you could always get the right answer, (from the form Ax^2 + Bx + C), but it's pretty time consuming and I'm not sure whether you've actually learned that yet..
hope that helps! :)
