Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below. If Kyle use
s 18 feet of wood to make the frame, what is the length of the frame?
1 answer:
Answer:
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6.75 feet |
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Step-by-step explanation:
Let the width be x. If the width is x, the the length has to be 3x because in the question it says that the length is 3 times the width.
Since this is a rectangle, the opposite side has the same measure, like in the attachment below.
To find the perimeter, you would add up all the sides.
3x+3x+x+x
=6x+2x
=8x
It is also given in the question that he uses 18 feet. Which means that the perimeter is 18 feet. But you figured out that 8x is ALSO the perimeter. This means that you can say: 8x=18.
Solve for x, 18/8=9/4=2.25.
You want the length, which is 3x. So 3(2.25) is your answer.
3(2.25) = 6.75
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Answer:
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Step-by-step explanation:
A is the intersection of angle bisectors, so is the incenter of triangle EFG. It is also the intersection of the perpendicular bisectors of the sides of triangle EFG, so is the circumcenter.
The altitudes at X, Y, and Z are perpendicular to sides EF, EG, and FG, and pass through the incenter, so X, Y, Z are points on the incircle.
A is the center of circles through E, F, and G, and through X, Y, and Z.
Answer: The time at which the distance between the two is 150 miles is 1.3 hr.
Step-by-step explanation:
Step 1: Sketch the problem as shown in the attached image.
The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.
It follows the equation x² + y² = 15².
The distance covered by Greg is given by <em>x mi</em>, and that of Erin is given by <em>y mi</em>.
Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>
Which by cross-multiplying gives <em>distance = speed × time</em>.
Let time taken to cover the distance be <em>t h</em>.
Given that Speed of Erin is 9 mph and that of Greg is 7 mph.
Hence, distance covered by Greg, x = 7 × t = 7t.
Distance covered by Erin, y = 9 × t = 9t.
Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for <em>time t.</em>
(7t)² + (9t)² = 15²
49t² + 81t² = 225
(49 + 81)t² = 225
t² = 225/(49 + 81)
t² = 225/130
t² = 1.730769231
t = √1.730769231
t = 1.315587029
t = 1.3hr
Hence the time at which the distance between the two is 150 miles is 1.3 hr.
