Which best describes the area of a polygon
2 answers:
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The triangle is drawn and is shown in the image attached with.
We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same.
D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:
AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units
So,
Therefore, the length of DE will be 3 units
We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same.
D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:
AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units
So,
Therefore, the length of DE will be 3 units
Answer:
(1, 8.5 ) and ( - 17, 80.5 )
Step-by-step explanation:
Given the 2 equations
y = x² + 4x + 4 → (1)
y = - 4x + 12 → (2)
Substitute (1) into (2), that is
x² + 4x + 4 = - 4x + 12
( multiply through by 2 to clear the fractions )
x² + 8x + 8 = - 8x + 25 ( add 8x to both sides )
x² + 16x + 8 = 25 ( subtract 25 from both sides )
x² + 16x - 17 = 0 ← in standard form
(x + 17)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 17 = 0 ⇒ x = - 17
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 equations and evaluate for y
Substituting into (2 )
x = 1 : y = - 4(1) + 12.5 = - 4 + 12.5 = 8.5 ⇒ (1, 8.5 )
x = - 17 : y = - 4(- 17) + 12.5 = 68 + 12.5 = 80.5 ⇒ (- 17, 80.5 )