Posted by **quintana** on Friday, July 12, 2013 at 5:59am.

if the altitude and the base of a triangle are each increased by 4 inches the area of the triangle will be increased by 42 square inches. if the altitude is increased by 3 inches and the base is decreased by 2 inches the area will be increased by 5 square inches. find the base and the altitude of the triangle.

- college algebra -
**Reiny**, Friday, July 12, 2013 at 9:20am
let original base be b and height be h

original area = bh/2

case1:

new base = b+4

new height = h+4

new area = (b+4)(h+4)/2 = bh/2 + 42

bh + 4b + 4h + 16 = bh + 84

4b + 4h = 68

b+h = 17 #1

case2:

new base = b-2

new height = h+3

new area = (b-2)(h+3)/2 = bh/2 + 5

bh + 3b - 2h - 6 = bh + 10

3b - 2h = 16 #2

#1 x 2 ---->2b+2h= 34

add to #2

5b = 50

b = 10

a = 7

original base is 10 inches

original height is 7 inches

check:

original area = 35

case1:

area = 14(11)/2 = 77 , it increased by 42

case2:

area = (10)(8)/2 = 40 , it increased by 5

all is good!

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