Two corners of an isosceles triangle are at $(9, 6)$ $(9 ,6 )$ and $(4, 7)$ $(4 ,7 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

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Answer 1 · 2017-09-28T11:08:20

The length of three sides of triangle are $5.1, 25.2, 25.2$ $5.1 ,25.2 , 25.2$ unit.

Base of the isocelles triangle is $B = \sqrt{{(x_{1} - x_{2})}_{1}^{2} + {(y_{1} - y_{2})}_{1}^{2}})$ $B= sqrt((x_1-x_2)^2+(y_1-y_2)^2))$

$= \sqrt{{(9 - 4)}^{2} + {(6 - 7)}^{2}}) = \sqrt{25 + 1} = \sqrt{26} = 5.1 (1 d p)$ $= sqrt((9-4)^2+(6-7)^2)) =sqrt(25+1)=sqrt26 =5.1 (1dp)$ unit

We know area of triangle is $A_{t} = \frac{1}{2} \cdot B \cdot H$ $A_t =1/2*B*H$ Where $H$ $H$ is altitude.

$:. 64=1/2*5.1*H or H= 128/5.1=25.1 (1dp)$ unit

Legs are $L = sqrt(H^2+(B/2)^2)$

$= sqrt( 25.1^2+(5.1/2)^2)=25.2(1dp)$ unit

The length of three sides of triangle are $5.1 ,25.2 , 25.2$ unit [Ans]

Two corners of an isosceles triangle are at (9 ,6 )(9,6)(9 ,6 ) and (4 ,7 )(4,7)(4 ,7 ). If the triangle's area is 64 6464 , what are the lengths of the triangle's sides?