Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length
of O M is 28, the length of M P is y, and the length of P N is 18.
Which value of y would make O P is parallel to L N?
16
24
32
36
Which value of y would make O P is parallel to L N?
16
24
32
36
2 answers:
Answer:
The value of y that would make O P parallel to L N = 36
Step-by-step explanation:
This is a question on similar triangles. Find attached the diagram obtained from the given information.
Given:
The length of O L = 14
the length of O M = 28
the length of M P = y
the length of P N = 18
Length MN = MP + PN = y + 18
Length ML = MO + OL = 28+14 = 42
For OP to be parallel to LN,
MO/ML = MP/PN
MO/ML = 28/42
MP/PN= y/(y+18)
28/42 = y/(y+18)
42y = 28(y+18)
42y = 28y + 18(28)
42y-28y = 504
14y = 504
y = 504/14 = 36
The value of y that would make O P parallel to L N = 36
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1. Draw an accurate picture of the triangle in
the coordinate axes, as shown in the attached picture.<span>
<span>2. Circumscribe a rectangle about the triangle, as shown in
the picture. The coordinates of the points M, N, T are easily identifiable as shown in the
picture.</span>
<span>3. The area of the triangle ABC is The area of
the rectangle - Area 1- Area 2- Area 3.</span>
Area 1 = 1/2(3*7)=21/2
Area 2 = 1/2(4*4)=1/2*16=8
<span>Area 3 = 1/2( 3*7)=21/2</span>
<span>Area 1+Area 2+Area 3=21/2+21/2+8=21+8=29 (units squared)</span>
<span>Area rectangle= 7*7=49 (units squared)</span>
<span>Answer: Area of triangle is 20 units squared.</span></span>
The picture in the attached figure
we know that
a) <span>∠1 and ∠5
are congruent-----> by corresponding angles
b) </span>∠3 and ∠8------> supplementary angles (∠3 + ∠8=180°)
<span>are not congruent
c)</span>∠6 and ∠4------> supplementary angles (∠6 + ∠4=180°)
are not congruent
d) ∠8 and ∠2------> supplementary angles (∠8 + ∠2=180°)
are not congruent
e) ∠4 and ∠7-----> supplementary angles (∠4 + ∠7=180°)
are not congruent
we know that
a) <span>∠1 and ∠5
are congruent-----> by corresponding angles
b) </span>∠3 and ∠8------> supplementary angles (∠3 + ∠8=180°)
<span>are not congruent
c)</span>∠6 and ∠4------> supplementary angles (∠6 + ∠4=180°)
are not congruent
d) ∠8 and ∠2------> supplementary angles (∠8 + ∠2=180°)
are not congruent
e) ∠4 and ∠7-----> supplementary angles (∠4 + ∠7=180°)
are not congruent