Two corners of an isosceles triangle are at $(8, 1)$ $(8 ,1 )$ and $(1, 4)$ $(1 ,4 )$ . If the triangle's area is $15$ $15$ , what are the lengths of the triangle's sides?

Question

Two corners of an isosceles triangle are at $(8, 1)$ $(8 ,1 )$ and $(1, 4)$ $(1 ,4 )$ . If the triangle's area is $15$ $15$ , what are the lengths of the triangle's sides?

1 Answer

Impact of this question

1318 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-30T11:16:33

Lengths of triangle's sides are $7.62, 5.48, 5.48$ $7.62 , 5.48 , 5.48$ unit

Explanation:

Base of the isosceles triangle is $b = \sqrt{{(x_{1} - x_{2})}_{1}^{2} + {(y_{1} - y_{2})}_{1}^{2}} = \sqrt{{(8 - 1)}^{2} + {(1 - 4)}^{2}} = \sqrt{58} = 7.62 (2 d p)$ $b=sqrt((x_1-x_2)^2+(y_1-y_2)^2) =sqrt((8-1)^2+(1-4)^2)=sqrt58=7.62(2dp)$

Area of the triangle is $A_{t} = \frac{1}{2} \cdot b \cdot h or h = \frac{2 \cdot A_{t}}{b} = \frac{2 \cdot 15}{7.62} = \frac{30}{7.62} = 3.94 (2 d p)$ $A_t =1/2*b*h or h= (2*A_t)/b = (2*15)/7.62=30/7.62=3.94(2dp)$ . where $h$ $h$ is altitude.

Legs are $l = \sqrt{h^{2} + {(\frac{b}{2})}^{2}} = \sqrt{{3.94}^{2} + {(\frac{7.62}{2})}^{2}} = \sqrt{30.04} = 5.48 (2 d p)$ $l= sqrt (h^2+(b/2)^2) = sqrt (3.94^2+(7.62/2)^2)=sqrt (30.04)=5.48(2dp)$

Lengths of triangle's sides are $7.62, 5.48, 5.48 (2 d p)$ $7.62 , 5.48 , 5.48 (2dp)$ unit[Ans]

Science

Math

Humanities

... and beyond

Two corners of an isosceles triangle are at $(8, 1)$ $(8 ,1 )$ and $(1, 4)$ $(1 ,4 )$ . If the triangle's area is $15$ $15$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Two corners of an isosceles triangle are at (8,1)(8 ,1 ) and (1,4)(1 ,4 ). If the triangle's area is 1515 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

Related questions

Impact of this question

Two corners of an isosceles triangle are at $(8, 1)$ $(8 ,1 )$ and $(1, 4)$ $(1 ,4 )$ . If the triangle's area is $15$ $15$ , what are the lengths of the triangle's sides?