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In the given figure, If we consider the side with 12 units as base & height as the one with 3 units, area = 12*3 -------------- (1) If we consider the side with 7 units as base & height as the one with x units, area = 7*x ----------------(2)
You can calculate the area of the triangle, using the side of length 12 as the base: (1/2)(12)(3) = 18
Next, use [color=#ff0000]the side of length 7 as the base and write the equation for the area: (1/2)(7)(x) = 18[/color] Now solve for x, the unknown height: 7x = 36 x = 36/7
Answer: C.
Hi Bunel, Could you kindly explain the highlighted portion in detail? I am not able to understand why you have equated that to 18? Thanks, Arun
You can calculate the area of the triangle, using the side of length 12 as the base: (1/2)(12)(3) = 18
Next, use [color=#ff0000]the side of length 7 as the base and write the equation for the area: (1/2)(7)(x) = 18[/color] Now solve for x, the unknown height: 7x = 36 x = 36/7
Answer: C.
Hi Bunel, Could you kindly explain the highlighted portion in detail? I am not able to understand why you have equated that to 18? Thanks, Arun
In the given triangle with solid lines, the area of the triangle = 0.5*base*height.
Now you need to understand that the height can be from any of the 3 vertices and the base will then be the side to which the height is perpendicular to.
In this case, the line with length 3 is the height for the base with length 12, giving you area of the triangle = 0.5*12*3 = 18
Similarly, for the same triangle, the area will also be = 0.5*7*x ...( as the side with x length is perpendicular to the 'base' with length 7 units).
For a particular triangle, the area MUST be the same irrespective of what base or height combination you choose.
I was trying to solve it with the solid line's length=7, will it be more clearly marked in the exam? After going through the solution i realized that they meant the Solid+dotted line length is equal to 7
I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!
I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!
CE = 3; AC = 7; AB = 12; BD = x.
Consider AB as a base of triangle ABC. The are = 1/2*base*height = 1/2*AB*CE = 1/2*12*3 = 18.
Now, consider AC as a base of the SAME triangle ABC. In this case the height is BD (perpendicular from B to extended base AC) The are = 1/2*base*height = 1/2*AC*BD = 1/2*7*x = 18 --> 36/7.
I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!
CE = 3; AC = 7; AB = 12; BD = x.
Consider AB as a base of triangle ABC. The are = 1/2*base*height = 1/2*AB*CE = 1/2*12*3 = 18.
Now, consider AC as a base of the SAME triangle ABC. In this case the height is BD (perpendicular from B to extended base AC) The are = 1/2*base*height = 1/2*AC*BD = 1/2*7*x = 18 --> 36/7.
Area of triangle = (1/2)(base)(height) IMPORTANT CONCEPT: we can use ANY of the three sides as our base.
So, for example, if we want to find the area of triangle ABC, we can use side AB as the base, or we can use side AC as the base, or we can use side BC as the base.
If we use side AB as the base, then the base has length 12 and the height is 3 So, area of triangle ABC = (1/2)(12)(3)
If we use side AC as the base, then the base has length 7 and the height is x So, area of triangle ABC = (1/2)(7)(x)
IMPORTANT: If we use side AB as the base, the area of the triangle will be the same as the area we get if we use side AC as the base.
So, (1/2)(12)(3) = (1/2)(7)(x) [solve for x] Divide both sides by 1/2 to get: (12)(3) = (7)(x) Divide both sides by 7 to get: 36/7 = x
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