# The height of a triangle is 4 feet more than four times the length of the base. The area is 24 square feet. Find the base and the height. Show your work and explain the steps you used to find the solution in order to receive full credit.

Answer: Use the given information to create equations to help solve the problem.
H= 4+ 4B
A=24 square feet

Know that the area of a triangle formula is 1/2 x b x h.
A=1/2 x b x h

Plug in the known values and solve for the base.
24= .5 x B x (4+4B)
48=B(4+4B)
48=4B+4B^2
12= B + B^2
0=B^2 + B -12
0=(B+4)(B-3)
B= -4, 3

This solution gives us two answers, so plug both into the formula to find the correct answer.
24=.5 x -4 x (4+4(-4))
48= -4 x (-12)
48=48

24= .5 x 3 x (4+4(3))
48= 3 x (4+12)
48= 3(16)
48=48

It looks like both work, so either answer is correct.

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Ralph sold brownies for \$0.20 a piece in order to buy baseball cards. If the cards cost \$0.36 per pack, and Ralph had no money left over after buying them, what is the least number of brownies he must have sold?

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5 questions for algebra: 1. Solve for r.
s=2πrh
_______________________________
A. 2πsh=r
B. s2π=r
C. s2πh=r
D. s2=r

2. Solve for c.
a(b − c)=d
___________________________
A. c=ab − d
--------
b
B. c=ab + d
---------
a
C. c=d − ab
----------
a
D. c=ab − d
---------
a
3. Solve for q.
s = 4p + 4q
_________________
q= s − 4p
q= s − 4p
--------
4

q= 4p − s
----------
4

q= s − 4p
--------
p
4. For a trapezoid, the following formula relates the area A, the two bases A and B, and the height H.
A=(a+b)2h
Solve for a.
A. a = 2A − b
---------
h
B. a= 2A/h + b
C. a= 2A/h − b
D. a= Ah/2 − b
5. The formula for the perimeter of a rectangle is P=2(l+w).
Solve for l.
l= p/2 − w
l= P/2 + w
l= p − w
---------
2
l= 2P − w