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Viefleur [7K]
3 years ago
13

Julius needs to determine how much information needs to be given about an isosceles triangle to be able to draw an isosceles tri

angle. He is looking at six different cases and is trying to determine if that amount of detail will allow him to construct just one isosceles triangle or if it allows for more than one isosceles triangle.
Mathematics
1 answer:
Brrunno [24]3 years ago
3 0

Answer:

Six cases are enough to construct more than one isosceles triangle

Step-by-step explanation:

An Isosceles triangle is a triangle in which at least two of it's sides are congruent.

If two of the three sides of a triangle are congruent, but the third side is of a different length, the triangle is isosceles.

If all three sides of the triangle are congruent, even though this is an equilateral triangle, it satisfies the condition of an isosceles, and it is ok to still it isosceles.

Julius might decide to split information for a better explanation, it doesn't matter the number of cases he has, but six cases should be enough to draw an isosceles triangle.

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Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and <br> x + 7y = 8
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\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y  = \frac{17}{14} } \atop {x+7y=8}} \right.

To solve this system by substitution, first isolate x in the second equation.

x+7y=8
x+7y-7y=8-7y
x=8-7y

Now, plug this expression (8-7y) for x in the top equation to solve for y.

\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}
3- \frac{21}{8} y+ \frac{1}{3} y= \frac{17}{24}
72-63y+8y=17
72-55y=17
-55y=17-72
-55y=-55
y=1

Now that you have y, plug it into the second equation and solve for x.

x+7y=8
x+7(1)=8
x+7=8
x=1

Last step is to plug your x- and y-values in to both equations to check your work.

\frac{3}{8} (1)+ \frac{1}{3} y= \frac{17}{24}

\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ;  \frac{1}{3} * \frac{8}{8} = \frac{8}{24}

\frac{9}{24} + \frac{8}{24} = \frac{17}{24}  <--True

1+7(1)=8
1+7=8   <--True

Answer:
x=1 \\ y=1
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