<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:
2n+8
Step-by-step explanation:
Answer:
Nearest ten-350
Nearest hundred-300
Step-by-step explanation:
#When rounding to the nearest ten, we look at the ones digits in a number:
- If the ones digit is 0, 1, 2, 3, or 4, you will round down to the previous ten
- If the ones digit is 5, 6, 7, 8, or 9, you will round up to the next ten
Given the number 348, 8 in the ones digit greater than 4 so we round to the next ten:
348 ≈350
#When rounding to the nearest hundred, we look at the tens digits in a number:
- If the ones digit is less than 5 you will round down to the previous hundred
- If the ones digit is greater than 4, you will round up to the next hundred
Given the number 348, 4 in the tens digit less than 5 so we round down to the previous hundred:
348 ≈300
Answer:
30 years old
Step-by-step explanation:
5x = x + 2(12)
5x = x + 24
4x = 24
x = 6
5(x)
5(6) = 30
Answer:
Let the number of nickels be x
Let the number of pennies be y
Let the number of dimes be z
Now z=x+y
FIrst equation:
z+x+y=16
Subsittue for z:
x+y+x+y=16
y=8-x (subsitution)
Hope this helps :)
Step-by-step explanation:
