<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>
Answer:
Frank's father waited 140 minutes all together
Step-by-step explanation:
Sorry if I'm wrong :/
Answer: 56.25 of 70% and 93.75pints of 90%
Step-by-step explanation: First find the ratios. One juice is 70% and the other is 95%. Your goal is 85%. This is 15% from 70 and 10% from 95. This means you need (15)/(15+10) of 95, which is 3/5 of all the juice to be 95. This means you will need more of the 95% juice, which makes sense because 85 is closer to 95. So 3:5 and total 150=56.25 of 70% and 93.75pints of 90%
Answer:
21.43 miles
Step-by-step explanation:
Let
x ---> the number of miles
y ---> the total cost of rent a car per day
we know that
The linear equation in slope intercept form is equal to
where
m is the slope
b is the y-intercept
we have
<em>sunshine rental company</em>
The slope is equal to
The y-intercept is equal to
substitute
----> equation A
<em> rent me company</em>
The slope is equal to
The y-intercept is equal to
substitute
----> equation B
equate equation A and equation B
solve for x
