The height and sides of a triangle are four consecutive integers. The height is the first integer, and the base is the 3rd interger. The perimeter of the triangle is 42 in. Find the area of the triangle.
Now, for all the future wise remarks, I do not typically do this for math homework, I've completed 29 of my 30 assigned problems... this is the only one I haven't solved yet.
2006-09-09 15:55:09 · 4 answers · asked by born2bfree 3 in Education & Reference ➔ Homework Help
Let the height measure x in.
Therefore, the other sides measure x+1, x+2, x+3.
x+1+x+2+x+3=42 in
3x+6=42
3x=36
x=12 in
Height=12 in
Base=x+2= 14 in
Area of triange= I/2X baseX height
=1/2X12X14= 84sq.in
2006-09-09 16:24:01 · answer #1 · answered by mj 2 · 0⤊ 0⤋
If the perimeter is 42, then the sides must be 13, 14, 15.
The height must be 12. 14 is the third integer, So, it must be (12*14)/2 or 84.
You make up two triangles in the larger one.
One is a 9, 12, 15 right triangle and the other is 5, 12, 13 right triangle. (that will really get your teacher's attention). How did I get these numbers?
If the Hypotenuse of one triangle is 15 and one side 12, using A^2+ B^2 = C^2 (good old Pythagoras) and substituting (12^2 + B^2 = 15^2 or 144 + B^2 = 225) B^2 is 81 or B= 9. The same can be done with sides 12 and 13. You will find that B^2 = 25 or B=5.
2006-09-09 23:05:03 · answer #2 · answered by SPLATT 7 · 0⤊ 0⤋
84=area
The lengths are 12, 13, 14 and 15.
It forms 2 right triangles, one with sides 12 and 5 and hypoteneuse 13 and the other 12, 9 with 15. The 5 and 9 are added to form the base.
2006-09-09 23:03:27 · answer #3 · answered by kengoward 3 · 0⤊ 0⤋
The area of the triangle is 126.I hope its right its been a while since i opened a math book.
2006-09-09 23:03:14 · answer #4 · answered by carolinafan 2 · 0⤊ 0⤋