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3 years ago

Find x. Side splitter theorem

Mathematics

1 answer:

professor190 [17]3 years ago

3 0

Answer:

x = 9

Step-by-step explanation:

The outer and inner triangles are similar, thus the ratios of corresponding sides are equal, that is

$\frac{8}{8+4}$ = $\frac{x-3}{x}$ , that is

$\frac{8}{12}$ = $\frac{x-3}{x}$ ( cross- multiply )

12(x - 3) = 8x

12x - 36 = 8x ( subtract 8x from both sides )

4x - 36 = 0 ( add 36 to both sides )

4x = 36 ( divide both sides by 4 )

x = 9

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Alexxandr [17]

Answer:Positive

Step-by-step explanation:

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2 years ago

What numbers that have the same sign equal -4 3/5

djverab [1.8K]

Answer:

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced A equals B.[1][2] The symbol "=" is called an "equals sign". Two objects that are not equal are said to be distinct.

Step-by-step explanation:

For example:

{\displaystyle x=y}x=y means that x and y denote the same object.[3]

The identity {\displaystyle (x+1)^{2}=x^{2}+2x+1}{\displaystyle (x+1)^{2}=x^{2}+2x+1} means that if x is any number, then the two expressions have the same value. This may also be interpreted as saying that the two sides of the equals sign represent the same function.

{\displaystyle \{x\mid P(x)\}=\{x\mid Q(x)\}}{\displaystyle \{x\mid P(x)\}=\{x\mid Q(x)\}} if and only if {\displaystyle P(x)\Leftrightarrow Q(x).}{\displaystyle P(x)\Leftrightarrow Q(x).} This assertion, which uses set-builder notation, means that if the elements satisfying the property {\displaystyle P(x)}P(x) are the same as the elements satisfying {\displaystyle Q(x),}{\displaystyle Q(x),} then the two uses of the set-builder notation define the same set. This property is often expressed as "two sets that have the same elements are equal." It is one of the usual axioms of set theory, called axiom of extensionality.[4]

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3 years ago

Read 2 more answers

In how many ways could a club of 29 appoint a committee of 4 people?

qwelly [4]

Answer:

7.25

Step-by-step explanation:

8 0

2 years ago

A= h(b+c) solve for b

madreJ [45]

A=h(b+c)
A/h=b+c
b=(A/h)-c

Answer: b=(A/h)-c

7 0

3 years ago

Read 2 more answers

∆ABC is an isosceles triangle. The length of CB is 12 feet 4 inches and the congruent sides are

son4ous [18]

Answer:

Answer for 2nd is option c, for 3rd is option d, for 4th is option e

Step-by-step explanation:

As we know 1 ft.=12 in.

In ΔABC

∴ The congruent sides are AB and AC respectively

CB =12 ft. 4 in.=148 in.
AB= $\frac{3}{4}$ CB =111 in. =9 ft. 3 in.
AC= $\frac{3}{4}$ CB =111 in. =9 ft. 3 in.

∵ Perimeter of ΔABC =AB+AC+CB

=9 ft. 3 in. + 9 ft. 3 in. +12 ft. 4 in.

=30 ft. 10 in.

2. In ΔDEF

∴ The congruent sides are DE and DF respectively

DE = 6 ft. 3 in. =75 in.
DF = 6 ft. 3 in. =75 in.
Let the length of FE is equal to x
0.75FE =DE =DF
0.75x = 6 ft. 3 in. =75 in.
x =100 in. =8 ft. 4 in.

∵ Perimeter of ΔDEF =DE+DF+FE

= 6 ft. 3 in. +6 ft. 3 in. +8 ft. 4 in.

= 20 ft. 10 in.

3. In ΔJKL

∴ The congruent sides are JL and KL respectively

JK = x+3
KL =4x-17
JL =6x-45
JL≅KL
4x-17 =6x-45 . . . . . . . . . . . . . . . . . . . . . . . (1)
Subracting 4x from both sides from eq 1
-17 =2x-45
Adding 45 on both the sides
28 =2x
Dividing by 2 on both sides
14 =x
JK = 14+3 =17
KL = 4×14-17 =39
JL = 6×14-45 =39

∵ The dimensions of the ΔJKL are 39,39 and 17.

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3 years ago