Pre-Algebra: "The area of a triangle is 144 square miles. The height is 8 square ..."

[mg4]

Pre-Algebra: "The area of a triangle is 144 square miles. The height is 8 square ..."

[FONT=&quot]My daughter recently took a math test and the following question was marked incorrect. Please answer and explain. Thank you.[/FONT]
[FONT=&quot]
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[FONT=&quot]The area of a triangle is 144 square miles. The height is 8 square miles. Find the length of the base.[/FONT]
[FONT=&quot]a. 138[/FONT]
[FONT=&quot]b. 36[/FONT]
[FONT=&quot]c. 18[/FONT]
[FONT=&quot]d. 0[/FONT]

 

[mmm4444bot]

Please answer and explain.

Hello, and welcome! We don't provide answer services, but we'd enjoy seeing her work. That's the best way, for tutors to see what went wrong. Can she reply with her steps?

Please check out the forum's guidelines, too. Thank you! :cool:

 

[Dr.Peterson]

My daughter recently took a math test and the following question was marked incorrect. Please answer and explain. Thank you.


The area of a triangle is 144 square miles. The height is 8 square miles. Find the length of the base.
a. 138
b. 36
c. 18
d. 0

Please be sure that you copy the problem correctly: a height can't be measured in square miles, so if this is what it said, the problem itself is wrong. Also, the units for the answer ought to have been stated, though it is not unreasonable to assume miles.

Also, as was mentioned, we want you to show her answer and her thinking, in order to help as effectively as possible.

 

[mg4]

Please be sure that you copy the problem correctly: a height can't be measured in square miles, so if this is what it said, the problem itself is wrong. Also, the units for the answer ought to have been stated, though it is not unreasonable to assume miles.

Also, as was mentioned, we want you to show her answer and her thinking, in order to help as effectively as possible.

The area of a triangle is 144 square miles. The height is 8 miles. Find the length of the base.
a. 138
b. 36
c. 18
d. 0

The problem was solved as follows:
Area = Base x Height
...................2
144 = B x 8
............2
Multiplying both sides by 2 gives us: 288 = 8B
Dividing both sides by 8 isolates for the variable giving us the base length; B = 36.

 

[Dr.Peterson]

The area of a triangle is 144 square miles. The height is 8 miles. Find the length of the base (in miles).
a. 138
b. 36
c. 18
d. 0

The problem was solved as follows:
Area = Base x Height
...................2
144 = B x 8
............2
Multiplying both sides by 2 gives us: 288 = 8B
Dividing both sides by 8 isolates for the variable giving us the base length; B = 36.

That is, of course, correct. With base 36 and height 8, the area is (36*8)/2 = 144.

Are you saying that answer was marked as incorrect? Clearly it was marked incorrectly.

 

[mg4]

That is, of course, correct. With base 36 and height 8, the area is (36*8)/2 = 144.

Are you saying that answer was marked as incorrect? Clearly it was marked incorrectly.

Yes. The answer was marked incorrectly and the following was provided by the teacher as an explanation.

"Thank you for supplying me with a further explanation of (child's name) answer to problem no.3 on the Chapter test.The question already states the area of the triangle as 144 square miles and the height is 8 miles.
144= 8 X height is the equation - divide both sides of the equation by 8. height = 18
Please picture a rectangle bisected by a diagonal to form two triangles, each with an area of 144 square miles.. The base of each triangle and the height of each triangle with be the same numbers for both triangles, but the area of the rectangle is both areas added together."

What am I missing here? Please advise and/or provide me with an appropriate response.
Thank you for your help.

 

[Dr.Peterson]

The answer you provided in the main forum was the answer my daughter selected; however, her teacher provided this response: "The question already states the area of the triangle as 144 square miles and the height is 8 miles. 144= 8 X height is the equation - divide both sides of the equation by 8. height = 18 Please picture a rectangle bisected by a diagonal to form two triangles, each with an area of 144 square miles.. The base of each triangle and the height of each triangle with be the same numbers for both triangles, but the area of the rectangle is both areas added together." What are we missing? I still believe the correct answer is 36. Your thoughts?

I'm replying here rather than to your private message, so others can see it.

I'm baffled. The question, as you quote it, is about a triangle, not the rectangle that has been described here. But what the teacher said can be used to obtain the correct answer: If each triangle has an area of 144 mi², then the area of the rectangle is 288 mi², so the equation to solve would be 288 = 8H, and again the answer is 36. The teacher is contradicting herself.

Unless you have quoted something wrong, the teacher is simply incorrect. I would want to meet face to face and draw the picture, showing what I said above.