One triangle on a graph has a vertical side of 5 and a horizontal side of 11. Another triangle on a graph has a vertical side of
15 and a horizontal side of 33.
Could the hypotenuses of these two triangles lie along the same line?
Could the hypotenuses of these two triangles lie along the same line?
1 answer:
Answer:
Yes.
Step-by-step explanation:
The two triangles are <em>similar</em> because they have:
- a common angle (90°)
- corresponding sides with lengths in a 3:1 ratio
All you need to do is to slide the smaller triangle into the larger one so that a small angle and one of its sides coincide.
Then the hypotenuses of each triangle will lie along the same line.
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The cost of 1 hamburger is $ 2.5 and cost of 1 fries is $ 0.8
<h3><u>Solution:</u></h3>Let "f" be the cost of 1 fries
Let "h" be the cost of 1 hamburger
<em><u>Given that, tennis coach took his team out for lunch and bought 8 hamburgers and 5 fries for $24</u></em>
8 x cost of 1 hamburger + 5 x cost of 1 fries = 24
8h + 5f = 24 -------- eqn 1
<em><u>The players were still hungry so the coach bought six more hamburgers and two more fries for $16.60</u></em>
6 x cost of 1 hamburger + 2 x cost of 1 fries = 16.60
6h + 2f = 16.60 ------ eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
Multiply eqn 1 by 2
16h + 10f = 48 ------ eqn 3
Multiply eqn 2 by 5
30h + 10f = 83 -------- eqn 4
<em><u>Subtract eqn 3 from eqn 4</u></em>
30h + 10f = 83
16h + 10f = 48
( - ) ----------------------
14h = 35
<h3>h = 2.5</h3>Substitute h = 2.5 in eqn 1
8(2.5) + 5f = 24
20 + 5f = 24
5f = 4
<h3>f = 0.8</h3>Thus cost of 1 hamburger is $ 2.5 and cost of 1 fries is $ 0.8