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2 years ago

Triangle KLM is similar to Triangle RST.

Mathematics

2 answers:

fgiga [73]2 years ago

8 0

Answer: true

Step-by-step explanation:

since the triangles are similar the sides are proportional

Alchen [17]2 years ago

4 0

Answer:

Step-by-step explanation:

When we demonstrate a similarity, we deduct corresponding congruences and proportions.

It's important to know that similarities are about proportional sides, but congruent angles.

So, if ΔKLM is similar to ΔRST, that means corresponding sides are proportional, which pairs of sides are corresponding? Well,

KL and RS.
LM and ST.

KM and RT.

SO, the proportional relation is

$\frac{KL}{RS}=\frac{LM}{ST}=\frac{KM}{RT}$

You can see this corresponding side in the image, KL is at the same position than RS, this also apply for LM and ST, KM and RT.

Therefore, the given statement is true.

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Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC

e-lub [12.9K]

Answer:

$DC=\frac{8}{3}\ units$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

<em>In the right triangle ABM</em>

Applying the Pythagorean Theorem

$BM^2=AB^2-AM^2$

we have

$AB=5\ units\\AM=x\ units$

substitute

$BM^2=5^2-x^2$

$BM^2=25-x^2$ -----> equation A

<em>In the right triangle BMC</em>

Applying the Pythagorean Theorem

$BM^2=BC^2-MC^2$

we have

$BC=7\ units\\MC=AC-AM=(9-x)\ units$

substitute

$BM^2=7^2-(9-x)^2$

$BM^2=49-(81-18x+x^2)$

$BM^2=49-81+18x-x^2$

$BM^2=-x^2+18x-32$ ----> equation B

equate equation A and equation B

$-x^2+18x-32=25-x^2$

solve for x

$18x=25+32\\18x=57\\\\x=\frac{57}{18}$

Simplify

$x=\frac{19}{6}$

<em>Find the length of DC</em>

$DC=AC-2x$

substitute the given values

$DC=9-2(\frac{19}{6})$

$DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units$

8 0

3 years ago

Kara did a survey to determine to study the types of pets that students in her school had. She surveyed 300 students and found t

julsineya [31]

Answer:

Step-by-step explanation:

Total Number of Students =300

Percentage who had cats, n(C) = 40%

Percentage who had both cats and dogs , $n(C \cap D)$ = 12%

Percentage who had neither cats nor dogs, $n(C \cup D)'$ =45%

Now:

Universal Set, $U = n(C)+n(D)-n(C \cap D)+n(C \cup D)'$

$100 = 40 + n(D)-12+45\\n(D)=100-73\\$Percentage of those who own dogs =27\%$

Therefore:

Number of Students who had dogs

=27% of 300

=81

3 0

3 years ago

Solution of 34x+95=3(14x+9)

ch4aika [34]

Answer:

34 X + 95 is equal to 3 into bracket 14 x 1 + 9 (close

Step-by-step explanation:

it it is the for the algebra of class 10th not for 7 for all other classes

3 0

2 years ago

Which of these numbers is prime? large 11, 15, 21, 27, 56

gizmo_the_mogwai [7]

11 is the only prime number. It's only multiples are 1 and itself

6 0

2 years ago

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Use the ratio table to solve the percent problem. What percent is 32 out of 80? 4% 32% 40% 80% ?.

attashe74 [19]

<u>The answer is 40%</u>

32 / 80 = 0.4000

.4000 * 100 = 40.00%

3 0

3 years ago

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