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Mathematics

1 answer:

Helga [31]3 years ago

3 0

1. Perimeter
22a + 2(6a + 8) -4 = p

[I got 22a from 12a + 10a]

2. If p = 250, what is a?

22a + 2(6a + 8) - 4 = 250
Distributive property
22a + 12a + 16 - 4 = 250
Add like terms
34a + 12 = 250
Subtract 12 by both sides
34a = 238
Divide 34 by both sides
a = 7

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N the diagram, the ratios of two pairs of corresponding sides are equal.

MaRussiya [10]

Answer:

$\angle N\cong \angle Z$

Step-by-step explanation:

Given:

In ΔLMN and ΔXYZ, $MN=3\,,\,LN=2\,,\,YZ=9\,,\,XZ=6$

To find: criteria that needs to be shown to prove ΔLMN $\sim$ ΔXYZ using SAS similarity theorem

Solution:

According to SAS Similarity Theorem, if two sides in one triangle are proportional to two sides in another triangle and the included angle between the sides are congruent, then the two triangles are said to be similar.

In ΔLMN and ΔXYZ,

$\frac{LN}{XZ}=\frac{2}{6}=\frac{1}{3}\\\frac{MN}{YZ}=\frac{3}{9}=\frac{1}{3}\\\therefore \frac{LN}{XZ}=\frac{MN}{YZ}$

So, ΔLMN $\sim$ ΔXYZ by SAS similarity theorem if $\angle N\cong \angle Z$

3 0

3 years ago

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Holding a ruler upright at arm’s distance (24 in.), Ronnie aligned the bottom of the ruler with a mark on the utility pole that

atroni [7]

Answer:

10 feet

Step-by-step explanation:

Drawing obviously not to scale but... Red segment is the ruler, at least the part between 5 and 6 inches, 1 inch long. Brown segment is the pole, ground to the top. Leftmost point is the eye, green line is the horizontal. The triangles are similar (AAA, the vertical lines are parallel), the ratio of the side is the same as the ratio of the heights. The height of the larger triangle (measured across the green line is

$40 yd \times 3\frac{ft}{yd} \times 12\frac{in}{ft}= 1440''$ .

Ratio of the height is then $1440\div24 = 60$ .

At this point the height of the pole is 60 times the length of the measure on the ruler, or 60 inches, that is 5 feet. Add the 5 feet the pole was starting from, it's 10 feet.