Question

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.

Answer 1

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!