Find the measures of the numbered angles in rhombus QRST.
1 answer:
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Answer:
x = 2√2
y = 2√6
Step-by-step explanation:
Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)
These will be equal since the triangles are similar
shorter leg : longer leg
(blue triangle = red triangle)
⇒ x : 4 = 2 : x
⇒ x/4 = 2/x
⇒ x² = 8
⇒ x = √8
⇒ x = 2√2
Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.
Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)
⇒ 4² + (2√2)² = y²
⇒ y² = 24
⇒ y = √24
⇒ y = 2√6
Part a.
<span>The perimeter formula is: </span>P = 2w + 2L
Your answer for part A is P = 2w + 2L
Part b.
They tell us in part b, that:
w = 6L + 20
Substitute that into what we got for part a.
P = 2(6L + 20) + 2L
P = 12L + 40 + 2L
P = 14L + 40
Your answer for partb is P = 14L + 40
Part c.
So we take what we got from part b, and solve for L.
P = 14L + 40
14L = P - 40
That is your answer for part 3 ^
part d.
Plug in w = 32 into what we first got in part b.
w = 6L + 20
32 = 6L + 20
6L = 12
L = 2
Your answer for part d is L = 2
<span>:D</span>
<span>The perimeter formula is: </span>P = 2w + 2L
Your answer for part A is P = 2w + 2L
Part b.
They tell us in part b, that:
w = 6L + 20
Substitute that into what we got for part a.
P = 2(6L + 20) + 2L
P = 12L + 40 + 2L
P = 14L + 40
Your answer for partb is P = 14L + 40
Part c.
So we take what we got from part b, and solve for L.
P = 14L + 40
14L = P - 40
That is your answer for part 3 ^
part d.
Plug in w = 32 into what we first got in part b.
w = 6L + 20
32 = 6L + 20
6L = 12
L = 2
Your answer for part d is L = 2
<span>:D</span>