Two corners of an isosceles triangle are at $(7, 9)$ $(7 ,9 )$ and $(5, 3)$ $(5 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

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Two corners of an isosceles triangle are at $(7, 9)$ $(7 ,9 )$ and $(5, 3)$ $(5 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

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Answer 1 · 2016-03-10T10:23:00

the sides are: $2 \sqrt{10} = 6.32456$ $2sqrt10=6.32456$
and $\frac{\sqrt{10490}}{5} = 20.4841$ $sqrt(10490)/5=20.4841$
and $\frac{\sqrt{10490}}{5} = 20.4841$ $sqrt(10490)/5=20.4841$

Explanation:

To compute for the sides, we need to obtain the height $h$ $h$ using the area $= 64$ $=64$ and the base $b$ $b$ that can be solved using the points (7, 9) and (5, 3)

We solve for the base first
$b = \sqrt{{(7 - 5)}^{2} + {(9 - 3)}^{2}}$ $b=sqrt((7-5)^2+(9-3)^2)$
$b = \sqrt{4 + 36} = \sqrt{40} = 2 \sqrt{10}$ $b=sqrt(4+36)=sqrt(40)=2sqrt10$

Area $= \frac{1}{2} \cdot b \cdot h$ $=1/2*b*h$
$64 = \frac{1}{2} \cdot 2 \cdot \sqrt{10} \cdot h$ $64=1/2*2*sqrt10*h$
$h = \frac{64}{\sqrt{10}} = \frac{32 \sqrt{10}}{5}$ $h=64/sqrt10=(32sqrt10)/5$

the height h divides the triangle into 2 equal parts and it passes thru the midpoint of the base b. So , we have a right triangle formed
Let x and x be the two unknown equal sides

$x = \sqrt{{(\frac{b}{2})}^{2} + h^{2}} = \sqrt{{(\frac{2 \sqrt{10}}{2})}^{2} + {(\frac{32 \sqrt{10}}{5})}^{2}}$ $x=sqrt((b/2)^2+h^2)=sqrt(((2sqrt10)/2)^2+((32sqrt10)/5)^2)$
$x = \sqrt{10 + \frac{1024 (10)}{25}} = \sqrt{\frac{250 + 10240}{25}}$ $x=sqrt(10+(1024(10))/25)=sqrt((250+10240)/25)$
$x = \sqrt{\frac{10490}{25}}$ $x=sqrt((10490)/25)$
$x = \frac{\sqrt{10490}}{5}$ $x=sqrt(10490)/5$
$x = 20.4841$ $x=20.4841" "$ units

God bless....I hope the explanation is useful.

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Two corners of an isosceles triangle are at $(7, 9)$ $(7 ,9 )$ and $(5, 3)$ $(5 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Two corners of an isosceles triangle are at (7,9)(7 ,9 ) and (5,3)(5 ,3 ). If the triangle's area is 6464 , what are the lengths of the triangle's sides?

1 Answer

Explanation:

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Impact of this question

Two corners of an isosceles triangle are at $(7, 9)$ $(7 ,9 )$ and $(5, 3)$ $(5 ,3 )$ . If the triangle's area is $64$ $64$ , what are the lengths of the triangle's sides?