SOLUTION: The area of a triangle is 35 square inches. The height of the triangle is 2 inches less than the base. What are the base and height of the triangle? Please help. I am so stuck!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The area of a triangle is 35 square inches. The height of the triangle is 2 inches less than the base. What are the base and height of the triangle? Please help. I am so stuck!      Log On


   

Question 602060: The area of a triangle is 35 square inches. The height of the triangle is 2 inches less than the base. What are the base and height of the triangle? Please help. I am so stuck!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+=+35+ in2
+A+=+%281%2F2%29%2Ab%2Ah+
+35+=+%281%2F2%29%2Ab%2Ah+
(1) +b%2Ah+=+70+
given:
(2) +h+=+b+-+2+ in
Substitute this into (1)
(1) +b%2A%28+b+-+2+%29+=+70+
(1) +b%5E2+-+2b+=+70+
Complete the square
(1) +b%5E2+-+2b+%2B+%28-2%2F2%29%5E2+=+70+%2B+%28-2%2F2%29%5E2+
(1) +b%5E2+-+2b+%2B+1+=+70+%2B+1+
(1) +%28+b+-+1+%29%5E2+=+71+
Take the square root of both sides
(1) +b+-+1+=+sqrt%2871%29+
(1) +b+=+1+%2B+sqrt%2871%29+ in
and
(2) +h+=+b+-+2+
(2) +h+=+-1+%2B+sqrt%2871%29+ in
check the answers:
+sqrt%2871%29+=+8.4261+
(1) +b+=+1+%2B+8.4261+
(1) +b+=+9.4261+
{2) +h+=+-1+%2B+8.4261+
(2) +h+=+7.4261+
and
+A+=+%281%2F2%29%2Ab%2Ah+
+A+=+.5%2A9.4261%2A7.4261+
+A+=+34.9996+
This looks close enough