SOLUTION: The height of a triangle is 4cm less the length of the base. If the area is 30 square cm, what is the height and length of base. I know the formula and I plugged in numbers to fi

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Question 131462: The height of a triangle is 4cm less the length of the base. If the area is 30 square cm, what is the height and length of base. I know the formula and I plugged in numbers to find the answers (6cm + 10cm), but I cannot prove it algebraicly.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For a triangle,
A+=+%281%2F2%29%2Ab%2Ah
A+=+30 cm2
h+=+b+-+4 cm
30+=+%281%2F2%29%2Ab%2A%28b+-+4%29
multiply both sides by 2
60+=+b%5E2+-+4b
b%5E2+-+4b+-+60+=+0
Complete the square
b%5E2+-+4b+%2B+%284%2F2%29%5E2+=+60+%2B+%284%2F2%29%5E2
%28b+-+2%29%5E2+=+64
b+-+2+=+8 (only the + square root makes sense here)
b+=+10
h+=+b+-+4
h+=+10+-+4
h+=+6
The base is 10 cm and the height is 6 cm
check:
A+=+30
A+=+%281%2F2%29%2Ab%2Ah
30+=+%281%2F2%29%2A10%2A6
30+=+30
OK