Triangle PQR and triangle XYZ are similar. The length of PQ= 4 inches, PR = 9 inches and QR = 12 inches. The length of the short
1 answer:
<em><u>Simplified </u></em><em><u>Recap:</u></em>
PQR and XYR are similar.
PQ: 4 inches (shortest side)
PR: 9 inches
QR: 12 inches (longest side)
<em><u>Solving:</u></em>
Because they are similar triangles, we know that the sides of one triangle are proportional to the ones on the other. Therefore, the smallest side of PQR is proportional to the smallest side of XYZ. Now, we just need to figure out the constant of proportionality , and we can do that by dividing the smallest side of XYZ triangle by the smallest side of PQR.
Now we know that the constant of proportionality is 4. All we have to do now is solve the problem. The question is asking what the longest side of XYZ is, and to find that we just need to multiply the longest side of PQR by our constant of proportionality.
Therefore, our answer is 48.
You might be interested in
Answer:
Width 150 meters.
Length = 350 meters.
Step-by-step explanation:
Let us assume the width of the fence = k meters
So, both sides = k + k = 2k meters
Also, the TOTAL fencing length = 600 m
So, the one side length of the fence = (600 - 2 k) meters
AREA = LENGTH x WIDTH
⇒ A(k) = (600 - 2k) (k)
or, A = -2k² + 600 k
The above equation is of the form: ax² +bx + C
Here: a = - 2 , b = 600 and C = 0
As a< 0, the parabola opens DOWNWARDS.
Here, x value is given as:
Solving for the value of k similarly, we get:
Thus the desired width = k = 150 meters
So, the desired dimensions of the plot is width 150 meters.
And length = 650 - 2k = 650 - 300 = 350 meters.
Answer:
Step-by-step explanation:
Any point on a given parabola is equidistant from focus and directrix.
Given:
Focus of the parabola is at .
Directrix of the parabola is .
Let be any point on the parabola. Then, from the definition of a parabola,
Distance of from focus = Distance of
from directrix.
Therefore,
Squaring both sides, we get
Hence, the equation of the parabola is .