SOLUTION: The base of a triangle is 4 dm longer than the altitude, and its area is 16 dm^2. Find the lengths of the base and the altitude.

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Question 1044245: The base of a triangle is 4 dm longer than the altitude, and its area is 16 dm^2. Find the lengths of the base and the altitude.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The base b of a triangle is c dm longer than the altitude h, and its area is A dm^2. Find the lengths of the base and the altitude.

system%28b=h%2Bc%2C%281%2F2%29bh=A%29

%281%2F2%29%28h%2Bc%29h=A
h%5E2%2Bch=A
h%5E2%2Bch-A=0
h=%28-c%2B-+sqrt%28c%5E2-4%2A%28-A%29%29%2F2%29
highlight%28h=%28-c%2Bsqrt%28c%5E2%2B4A%29%29%2F2%29


b=h%2Bc
b=%28-c%2Bsqrt%28c%5E2%2B4A%29%29%2F2%2Bc
b=-c%2F2%2Bsqrt%28c%5E2%2B4A%29%2F2%2B2c%2F2
highlight%28b=%28c%2Bsqrt%28c%5E2%2B4A%29%29%2F2%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The base of a triangle is 4 dm longer than the altitude, and its area is 16 dm^2. Find the lengths of the base and the altitude.
Let altitude be A

Then base = A + 4

We then get: %281%2F2%29+%2A+%28A+%2B+4%29A+=+16

%281%2F2%29+%2A+%28A%5E2+%2B+4A%29+=+16

%28A%5E2+%2B+4A%29%2F2+=+16

A%5E2+%2B+4A+=+32 ------ Cross-multiplying 

A%5E2+%2B+4A+-+32+=+0

(A - 4)(A + 8) = 0