Two corners of an isosceles triangle are at $(2, 4)$ $(2 ,4 )$ and $(3, 8)$ $(3 ,8 )$ . If the triangle's area is $48$ $48$ , what are the lengths of the triangle's sides?

Question

Two corners of an isosceles triangle are at $(2, 4)$ $(2 ,4 )$ and $(3, 8)$ $(3 ,8 )$ . If the triangle's area is $48$ $48$ , what are the lengths of the triangle's sides?

1 Answer

Impact of this question

1553 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-19T08:10:51

$Lengths of the sides of the triangle are$ $color(maroon)("Lengths of the sides of the triangle are "$

$a = b = 23.4, c = 4.12$ $color(indigo)(a = b = 23.4, c = 4.12$

Explanation:

![http://www.algebra.com/algebra/homework/Geometry-proofs/Geometry_proofshttp://.faq.question.209023.html](https://useruploads.socratic.org/zwonrgLRSdCBPBNldBqq_isosceles%20triangle.png)

$A (2, 4), B (3, 8), Area A_{t} = 48, To find AC, BC$ $A (2,4), B (3,8), " Area "A_t = 48, " To find AC, BC"$

$- - \to A B = c = \sqrt{{(2 - 3)}^{2} + {(4 - 8)}^{2}} = 4.12$ $vec(AB) = c = sqrt((2-3)^2 + (4-8)^2) = 4.12$

$A_{t} = (\frac{1}{2}) (A B) \cdot (C D)$ $A_t = (1/2) (AB) * (CD)$

$- - \to C D = h = \frac{2 \cdot 48}{4.12} = 23.3$ $vec(CD) = h = (2 * 48) / 4.12 = 23.3$

$Applying Pythagoras Theorem,$ $color(crimson)("Applying Pythagoras Theorem,"$

$- - \to A C = - - \to B C = b = \sqrt{h^{2} + {(\frac{c}{2})}^{2}}$ $vec(AC) = vec(BC) = b = sqrt(h^2 + (c/2)^2)$

$b = \sqrt{{23.3}^{2} + {(\frac{4.12}{2})}^{2}} = 23.4$ $b = sqrt(23.3^2 + (4.12/2)^2) = 23.4$

$a = b = 23.4, c = 4.12$ $color(indigo)(a = b = 23.4, c = 4.12$

Science

Math

Humanities

... and beyond

Two corners of an isosceles triangle are at $(2, 4)$ $(2 ,4 )$ and $(3, 8)$ $(3 ,8 )$ . If the triangle's area is $48$ $48$ , 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 (2,4)(2 ,4 ) and (3,8)(3 ,8 ). If the triangle's area is 4848 , 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 $(2, 4)$ $(2 ,4 )$ and $(3, 8)$ $(3 ,8 )$ . If the triangle's area is $48$ $48$ , what are the lengths of the triangle's sides?