Answer:
SteLet a = short leg of the right triangle, b = the longer leg, and c = the hypotenuse.
The longer leg of a right triangle is 4inches longer than the shorter leg: b = a + 4
The hypotenuse is 8inches longer than the shorter leg: c = a + 8
Use the Pythagorean Theorem:
a2 + b2 = c2
a2 + (a+4)2 = (a+8)2
a2 + a2 + 8a + 16 = a2 + 16a + 64
a2 - 8a - 48 = 0
Factors to:
(a-12)(a+4) = 0
a = 12, -4
Since we can't have a side of -4, a = 12
Shorter Leg = 12 inches
Longer Leg = 12 + 4 = 16 inches
Hypotenuse = 12 + 8 = 20 inches
Rewrite so
x
is on the left side of the inequality.
12
+
8
x
−
3
x
≥
5
+
2
x
−
2
Subtract
3
x
from
8
x
.
12
+
5
x
≥
5
+
2
x
−
2
Subtract
2
from
5
.
12
+
5
x
≥
2
x
+
3
Move all terms containing
x
to the left side of the inequality.
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12
+
3
x
≥
3
Move all terms not containing
x
to the right side of the inequality.
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3
x
≥
−
9
Divide each term by
3
and simplify.
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x
≥
−
3
The result can be shown in multiple forms.
Inequality Form:
x
≥
−
3
Interval Notation:
[
−
3
,
∞
)
