k4lnamja wrote:
Apologies
Can someone explain why we are adding 2ab?
I don't understand that part.
Cheers
No need to be apologetic k4lnamja. You can ask any question so far it's related to the topic.
We are dealing with a right angle triangle;
We are given its area and the hypotenuse and we are asked for perimeter.
Right angle triangle has three sides; one of which is hypotenuse. If we know the length of the other two, we will have the perimeter. However, there is no way to find out the length of the other two sides individually. Thus, our intention is to find the combined length of the other two sides and add it up with the hypotenuse to get the perimeter.
How can we use the information to know the combined length of the other two sides. Here's how.
Hypotenuse = c = 12
Let the other two sides of the right angle triangle be "a" and "b" and we know these two sides are perpendicular to each other.
Area = 28
Area of a triangle = 1/2*base*height = 1/2*a*b
1/2*a*b=28
a*b=56
c=12
As per pythagoras:
a^2+b^2=c^2
(a+b)^2-2ab=c^2
(a+b)^2-2*56=12^2
(a+b)^2-112=144
(a+b)^2=256
a+b=16
Thus, we know the sum of other two sides.
a+b=16
c=12
a+b+c=16+12=28
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Ans: "C"
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Just to expand the formula used:
(a+b)^2=a^2+b^2+2ab
(a+b)^2-2ab=a^2+b^2
(a+b)^2-2ab=c^2
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