Tobi
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$1/h
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I love math and am here for you to solve any mathematic questions
- Mathematics
- Algebra
- Logic
- Precalculus & Calculus
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About Tobi
I hate to suffocate my feet inside shoes, so you will often see me roaming around barI don't like to celebrate my birthdays.
I think I'm too afraid of celebrations, that is why you will rarely see me carousing at parties, etc.
As to WHY... I don't know yet. One fine morning I was introspecting as why can't I be normal like everyone else and enjoy birthdays, parties, dancing, etc. After much deliberation a voice came from the deep sub-conscious.. 'You are scared of celebrations, Atul!' I gasped in utter disbelief. I sat there for few minutes, only to realize to my horror that it was every bit TRUE! OK, don't psycho-analyze me too much!e-footed
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English
A triangular shaped lake-front lot has a perimeter of 1,800 ft. One side is 100 feet longer than the shortest side, while the third side is 200 feet longer than the shortest side. What are the leng...
Answer: Word Problems:
Word problems benefit most from translating words into algebraic expressions. The key is in reading the problem several times in order to understand the full context of the problem. Then identify the unknowns and how they are related before translating them into algebraic expressions.
Answer and Explanation:
The problem give the perimeter of the triangular lot as
P
=
1
,
800
ft
. Let
x
represent the shortest side of the lot and translate the descriptions into algebraic expressions:
One side is 100 feet longer than the shortest side
=
y
=
x
+
100
the third side is 200 feet longer than the shortest side
=
z
=
x
+
200
(Eq. 1)
(Eq. 2)
The problem give the perimeter of the triangular lot as
P
=
1
,
800
ft
and since the perimeter of a triangle is the sum of the lengths of its sides:
P
=
x
+
y
+
z
(Eq. 3)
Substituting Eq. 1, Eq. 2 and the value of the perimeter in Eq. 3, the length of the shortest side
x
is:
P
=
x
+
y
+
z
1
,
800
=
x
+
(
x
+
100
)
+
(
x
+
200
)
1
,
800
=
x
+
x
+
x
+
100
+
200
1
,
800
−
300
=
3
x
3
x
3
=
1
,
500
3
x
=
500
ft
(Eq. 3)
Substituting this value in Eq. 1 and Eq. 2, the lengths of the other sides of the triangular lot are:
y
=
x
+
100
z
=
x
+
200
y
=
500
+
100
z
=
500
+
200
y
=
600
ft
z
=
700
ft
Thus, the lengths of the three sides of the triangular lot are
500
ft
,
600
ft
and
700
ft
.
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