Two corners of an isosceles triangle are at #(8 ,5 )# and #(6 ,1 )#. If the triangle's area is #15 #, what are the lengths of the triangle's sides?

Answer 1

The length of three sides of triangle are #2sqrt5 ,5sqrt2 ,5sqrt2# unit

Base of the isocelles triangle is #B= sqrt((x_2-x_1)^2+(y_2-y_1)^2)) = sqrt((8-6)^2+(5-1)^2)) =sqrt(4+16)=sqrt20 =2sqrt5#unit

We know area of triangle is #A_t =1/2*B*H# Where #H# is altitude. #:. 15=1/cancel2*cancel2sqrt5*H or H= 15/sqrt5#unit

Legs are #L = sqrt(H^2+(B/2)^2)= sqrt(( 15/sqrt5)^2+((cancel2sqrt5)/cancel2)^2)=sqrt(45+5) = sqrt 50 = 5sqrt2 #unit

The length of three sides of triangle are #2sqrt5 ,5sqrt2 ,5sqrt2# unit [Ans]

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Answer 2

Theodore Abad

The lengths of the triangle's sides are approximately 5.39, 5.39, and 4.81 units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.