Vicky drew a scale drawing of a city. She used the scale 1 inch : 2 yards. If the actual width of a neighborhood park is 62 yard
1 answer:
Answer:
The park is <u>31 inches</u> wide in the drawing.
Step-by-step explanation:
Given:
Vicky drew a scale drawing of a city. She used the scale 1 inch : 2 yards.
The actual width of a neighborhood park is 62 yards.
Now, to find the width of park in drawing.
Let the width of park in drawing be
The scale drawing of the city is 1 inch : 2 yards.
So, 1 inch is equivalent to 2 yards.
Thus, is equivalent to 62 yards.
Now, to get the width of park in drawing by using cross multiplication method:
By cross multiplying we get:
Dividing both sides by 2 we get:
Therefore, the park is 31 inches wide in the drawing.
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Answer:
See Below.
Step-by-step explanation:
We are given the isosceles triangle ΔABC. By the definition of isosceles triangles, this means that ∠ABC = ∠ACB.
Segments BO and CO bisects ∠ABC and ∠ACB.
And we want to prove that ΔBOC is an isosceles triangle.
Since BO and CO are the angle bisectors of ∠ABC and ∠ACB, respectively, it means that ∠ABO = ∠CBO and ∠ACO = ∠BCO.
And since ∠ABC = ∠ACB, this implies that:
∠ABO = ∠CBO =∠ACO = ∠BCO.
This is shown in the figure as each angle having only one tick mark, meaning that they are congruent.
So, we know that:
∠ABC is the sum of the angles ∠ABO and ∠CBO. Likewise, ∠ACB is the sum of the angles ∠ACO and ∠BCO. Hence:
Since ∠ABO =∠ACO, by substitution:
Subtracting ∠ABO from both sides produces:
So, we've proven that the two angles are congruent, thereby proving that ΔBOC is indeed an isosceles triangle.
The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
<h3>How to determine the length</h3>The cosine rule is given as;
c = length of the diagonal
a = base length = 22 feet
b = 7 feet
feet
Using sine rule
Cross multiply
×
=
×
×
=
×
a = 18. 7 feet long
Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
Learn more about isosceles trapezoid here:
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