<em>Question:</em>
The area of the kite is 48 cm². What are the lengths of the diagonals PR and QS?
________
<em>Solution:</em>
You can split the kite into two isosceles triangles: PSR and PQR.
Assume that both diagonals intersect each other at the point O.
• Area of the triangle PSR:
m(PR) · m(OS)
A₁ = ————————
2
(x + x) · x
A₁ = ——————
2
2x · x
A₁ = ————
2
A₁ = x² (i)
• Area of the triangle PQR:
m(PR) · m(PQ)
A₂ = ————————
2
(x + x) · 2x
A₂ = ——————
2
2x · 2x
A₂ = ————
2
4x²
A₂ = ———
2
A₂ = 2x² (ii)
So the total area of the kite is
A = A₁ + A₂ = 48
Then,
x² + 2x² = 48
3x² = 48
48
x² = ———
3
x² = 16
x = √16
x = 4 cm
• Length of the diagonal PR:
m(PR) = x + x
m(PR) = 2x
m(PR) = 2 · 4
m(PR) = 8 cm
<span>• </span>Length of the diagonal SQ:
m(SQ) = x + 2x
m(SQ) = 3x
m(SQ) = 3 · 4
m(SQ) = 12 cm
I hope this helps. =)
Tags: <em>polygon area triangle plane geometry</em>
The frictional force between the tires and the road prevent the car from skidding off the road due to centripetal force.
If the frictional force is less than the centripetal force, the car will skid when it navigates a circular path.
The diagram below shows that when the car travels at tangential velocity, v, on a circular path with radius, r, the centripetal acceleration of v²/ r acts toward the center of the circle.
The resultant centripetal force is (mv²)/r, which should be balanced by the frictional force of μmg, where μ = coefficient of kinetic friction., and mg is the normal reaction on a car with mass, m.
This principle is applied on racing tracks, where the road is inclined away from the circle to give the car an extra restoring force to overcome the centripetal force.
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Answer:
x = 158
y = 22
Step-by-step explanation:
A triangle's inside sides sum up to 180 degrees. So to find the angle y, just take 180 - the sum of the other two sides.
70 + 88 = 158
180 - 158 = 22
y = 22 degrees
Now, to find angle x, since x and y are next to each other on a straight line, it means they are supplementary angles. Supplementary angles add together to equal 180, so just substract y from 180 to get x.
180 - 22 = 158
x = 158 degrees
