Question

Two corners of an isosceles triangle are at `(2 ,6 )` and `(4 ,8 )`. If the triangle's area is `48`, what are the lengths of the triangle's sides?

Answer 1

By using distance formula,then carry the procedure as usual

Explanation:

Using the DISTANCE FORMULA, we calculate the length of that side of the triangle.
(2,6) (4,8) : Using distance formula,
`sqrt((4-2)^2+(8-6)^2)` to obtain the length.
Then, we make use of the formula of Area of Triangle;

Area of Triangle=1/2BaseHeight
We replace the values that we have and the side which we had obtained previously -->>
`48=1/2*sqrt(8)*Height`
Height=48 units
We divide the sketch of an isoceles triangle into two parts

Then, make use of Pythagoras' Theorem, the idea of a right angled triangle :

The side obtained at first is divided into two equal parts , that is, `sqrt(8)/2` = 1
Then,theapplication of the formula below is made : `hyp=sqrt((opp^2+adj^2))`
(N.B:the hyp is representing one side of the two equal sides of the isoceles triangle)

By replacing the values in the equation, one of the equal sides has been found.. Therefore, two of the sides are the answer usind the Pythagoras' Theorem and the third one, the height obtained before...