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Fynjy0 [20]
3 years ago
14

a triangle has a base that is 3 times longer than its height. it has a area of 486 sq cm. what is the base and height

Mathematics
1 answer:
saw5 [17]3 years ago
6 0
B = 3h . . . . . . . .given by the problem statement
A = (1/2)bh . . . . formula for the area of a triangle

486 cm² = (1/2)*(3h)*h . . . substitute given information
(2/3)*486 cm² = h² . . . . . .multiply by 2/3
√324 cm = h . . . . . . . . . . . . . .take the square root

The height is 18 cm.
The base is 3*18 = 54 cm.
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Carter draws one side of equilateral △PQR on the coordinate plane at points P(-3,2) and Q(5,2). Which ordered pair is a possible
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Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

pq =    \sqrt{( {x2 - x1)}^{2}  + ( {y2 - y1)}^{2} }

or \:  \sqrt{( {5  + 3)}^{2} + ( {2 - 2)}^{2}  }

By simplifying it we get,

8

Now,

again finding the distance between PR,

pr = \sqrt{( {x2 - x1}^{2}  + ( {y2 - y1)}^{2} }

or,

\sqrt{( {x + 3)}^{2}  + ( {y - 2)}^{2} }

By simplifying it we get,

=  \sqrt{ {x}^{2} +  {y}^{2} + 6x  -  4y + 13  }

now, finding the distance of QR,

qr =  \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2}  }

or, by simplification we get,

\sqrt{ {x}^{2} +  {y}^{2}  - 10x - 4y + 29 }

now, equating PR and QR,

\sqrt{ {x}^{2} +  {y}^{2}  + 6x  -  4y  + 13}  =  \sqrt{ {x}^{2}  +  {y}^{2} - 10x - 4y + 29 }

we cancelled the root ,

{x}^{2} +  {y}^{2} + 6x - 4y + 13 =  {x}^{2}   +  {y}^{2}   -10x - 4y + 29

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

\sqrt{ {x}^{2} +  {y}^{2}  + 6x - 4y + 13 }  =  8}

cancel the roots,

{x}^{2} +  {y}^{2}   + 6x - 4y + 13  = 8

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

<em>Hope it helps</em><em>.</em><em>.</em><em>.</em>

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