Using the 28/36 ratio, determine the maximum allowable recurring debt for someone with a monthly income of $3,200. a. $256 b. $5
2 answers:
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The midpoint theorem states that the line joining the mid points of two sides of a triangle is parallel to the third and facing side and equal to half of the length of the third side
Based on the midpoint theorem, the area of triangle ΔLPQ is 63 square units
The reason the value of the area of triangle ΔLPQ as given above is correct is as follows:
The given parameters;
The midpoint of = M; The midpoint of
= N; The midpoint of
= O
The midpoint of = P; The midpoint of
= Q; The midpoint of
= R
The area of triangle ΔPQR = 21
The required parameter:
Calculate the area of triangle ΔLPQ
Method:
The definition of midpoint, area ratio, and area of a triangle formula can be used to find the area of triangle ΔLPQ
Solution:
According to the midpoint theorem, we have;
= (1/2) ×
= (1/2) ×
= (1/2) ×
Given that is parallel to
, and
is parallel to, we have;
∠MON = ∠PRQ
Similarly, we have, ∠MNO = ∠PQR
Therefore, ΔPQR is similar to triangle ΔMON, which is also similar to ΔJKS
The area of triangle ΔPQR = 21, by area ratio = (Side ratio)², we have;
The sides of ΔMON = 2 × The side length of ΔPQR
The area of triangle ΔMON = 2² × The area of ΔPQR
∴ The area of triangle ΔMON = 4 × 21
Similarly the area of ΔJKS = 4 × 4 × 21
PQ = JK/4
The area of LPQ = (1/2) × PQ × h
h = (3/4×JL) × sin(x°)
∴ The area of LPQ = (1/2)×JK/4×(3/4×JL) × sin(x°)
However; (1/2)×JK×JL× sin(x°) = Area of ΔJKS = 4 × 4 × 21
Therefore;
The area of ΔLPQ = (Area of ΔJKS)/4×(3/4) = (4 × 4 × 21)/4×(3/4) = 63
The area of triangle ΔLPQ = 63 square units
Learn more about the midpoint theorem here:
To solve this question we will use two important formulas.
The first formula involves the calculation of the decay constant, which is to be found as:
where is the half life of Pb-210 which is given to be 22 years in the question.
Thus,
Now, we will use the second formula which is called the function of decay formula and is given as:
where percentage of Pb-210 remaining in the bone at present, which in our case is 67% or 0.67
percentage of Pb-210 to start with, which is always 100% or 1.
Plugging in all these values in the decay formula we are supposed to find the time, .
Taking natural log on both sides we get:
years
Therefore the bone fragment is about 12.71 years old.