Answer:
Step-by-step explanation:
i
Dixon is 6 feet tall, Ariadne is 4 feet tall by proportion.
What in mathematics is a proportion?
- A proportion is an equation that sets two ratios at the same value.
- For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
We can use the proportion.
We already know that Dixon is 6 ft tall and that his shadow is 9 ft long.
Also we know that the shadow of his sister is 6 ft long.
6 : x = 9 : 6, or 6 / x = 9 / 6.
After that we will cross multiply : 9 * x = 6 * 6,
9 x = 36 ,
x = 36 /9,
x = 4.
Ariadne is 4 feet tall.
Learn more about proportion
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The complete question is -
Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixon's shadow is 9 feet long and Ariadne's shadow is 6 feet long. If Dixon is 6 feet tall, how tall is Ariadne?
Answer:
x = 20
y = 7.2
Step-by-step explanation:
12/x = 9/15
9x = 180
x = 20
12/x= y/12
12/20 = y/12
144 = 20y
y = 7.2
y = 20
<u>Part</u><u> </u><u>(</u><u>i</u><u>)</u>
1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)
2) Angles ABC and CDE are right angles (perpendicular lines form right angles)
3) Angles ABC and CDE are equal (all right angles are equal)
4) Angles ACB and DCE are equal (vertical angles are equal)
5) Triangles ABC and EDC are congruent (ASA)
<u>Part</u><u> </u><u>(</u><u>ii</u><u>)</u>
6) AB = DE (corresponding parts of congruent triangles are equal)
