Triangle A has a height of 2.5\text{ cm}2.5 cm2, point, 5, start text, space, c, m, end text and a base of 1.6\text{ cm}1.6 cm1, point, 6, start text, space, c, m, end text. The height and base of triangle B are proportional to the height and base of triangle A.
Answers
Answer:
Answer:
A)Height: 2.75 CM
Base: 1.76 CM
D)Height: 1.25 cm
Base:0.8 cm
E) height: 2 cm
base: 1.28 cm
Step-by-step explanation:
The complete question is
Triangle A has a height of 2.5 cm and a base of 1.6 cm The height and base of triangle B are proportional to the height and base of triangle A.
Which of the following could be the height and base of triangle B?
Choose 3 answers:
A)Height: 2.75 CM
Base: 1.76 CM
B) Height :9.25 cm
Base:9.16 cm
C)Height: 3.2 cm
base: 5 cm
D)Height: 1.25 cm
Base:0.8 cm
E) height: 2 cm
base: 1.28 cm
we know that
If the height and base of triangle B are proportional to the height and base of triangle A, then their ratios of the height to the base must be equal
step 1
Find out the ratio of the height to the base of triangle A
so
\frac{2.5}{1.6}= 1.56251.62.5=1.5625
step 2
Verify the ratio of the height to the base of each case and then compare with ratio of triangle A
A)Height: 2.75 CM
Base: 1.76 CM
\frac{2.75}{1.76}= 1.56251.762.75=1.5625
Compare
1.5625= 1.56251.5625=1.5625
therefore
Could be the height and base of triangle B
B) Height :9.25 cm
Base:9.16 cm
\frac{9.25}{9.16}= 1.00989.169.25=1.0098
Compare
1.0098 \neq 1.56251.0098=1.5625
therefore
It couldn't be the height and base of the B triangle.
C) Height: 3.2 cm
base: 5 cm
\frac{3.2}{5}= 0.6453.2=0.64
Compare
0.64 \neq 1.56250.64=1.5625
therefore
It couldn't be the height and base of the B triangle.
D)Height: 1.25 cm
Base:0.8 cm
\frac{1.25}{0.8}= 1.56250.81.25=1.5625
Compare
1.5625= 1.56251.5625=1.5625
therefore
Could be the height and base of triangle B
E) height: 2 cm
base: 1.28 cm
\frac{2}{1.28}= 1.56251.282=1.5625
Compare
1.5625= 1.56251.5625=1.5625
therefore
Could be the height and base of triangle B
Answer: the Answer is A D and E
Step-by-step explanation:
Triangle B is proportional to triangle A. That means that if we multiply one length from triangle A by a scale factor to get the length of the corresponding measurement of triangle B, we need to multiply the other length from triangle A by the same scale factor.
Hint #22 / 7
Triangle A Triangle B
Height (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 2.52.52, point, 5 \begin{array}{c}\small \blueD{\times 1.1}\\\LARGE\longrightarrow\end{array}
×1.1
⟶
2.752.752, point, 75
Base (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 1.61.61, point, 6 \begin{array}{c}\small \LARGE\longrightarrow\\\blueD{\times 1.1}\end{array}
⟶
×1.1
1.761.761, point, 76
Yes, if triangle B had a height of 2.75\,\text{cm}2.75cm2, point, 75, start text, c, m, end text, it would have a base of 1.76\,\text{cm}1.76cm1, point, 76, start text, c, m, end text.
Hint #33 / 7
Triangle A Triangle B
Height (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 2.52.52, point, 5 \begin{array}{c}\small \greenD{\times 3.7}\\\LARGE\longrightarrow\end{array}
×3.7
⟶
9.259.259, point, 25
Base (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 1.61.61, point, 6 \begin{array}{c}\small \LARGE\longrightarrow\\\greenD{\times 3.7}\end{array}
⟶
×3.7
5.925.925, point, 92
No, if triangle B has a height of 9.25\,\text{cm}9.25cm9, point, 25, start text, c, m, end text, then its base cannot be 9.16\,\text{cm}9.16cm9, point, 16, start text, c, m, end text long.
Hint #44 / 7
Triangle A Triangle B
Height (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 2.52.52, point, 5 \begin{array}{c}\small \purpleD{\times 1.28}\\\LARGE\longrightarrow\end{array}
×1.28
⟶
3.23.23, point, 2
Base (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 1.61.61, point, 6 \begin{array}{c}\small \LARGE\longrightarrow\\\purpleD{\times 1.28}\end{array}
⟶
×1.28
2.0482.0482, point, 048
No, if triangle B has a height of 3.2\,\text{cm}3.2cm3, point, 2, start text, c, m, end text, then its base cannot be 5\,\text{cm}5cm5, start text, c, m, end text long.
Hint #55 / 7
Triangle A Triangle B
Height (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 2.52.52, point, 5 \begin{array}{c}\small \maroonD{\times 0.5}\\\LARGE\longrightarrow\end{array}
×0.5
⟶
1.251.251, point, 25
Base (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 1.61.61, point, 6 \begin{array}{c}\small \LARGE\longrightarrow\\\maroonD{\times 0.5}\end{array}
⟶
×0.5
0.80.80, point, 8
Yes, if triangle B had a height of 1.25\,\text{cm}1.25cm1, point, 25, start text, c, m, end text, it would have a base of 0.8\,\text{cm}0.8cm0, point, 8, start text, c, m, end text.
Hint #66 / 7
Triangle A Triangle B
Height (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 2.52.52, point, 5 \begin{array}{c}\small \goldD{\times 0.8}\\\LARGE\longrightarrow\end{array}
×0.8
⟶
222
Base (\text{cm})(cm)left parenthesis, start text, c, m, end text, right parenthesis 1.61.61, point, 6 \begin{array}{c}\small \LARGE\longrightarrow\\\goldD{\times 0.8}\end{array}
⟶
×0.8
1.281.281, point, 28
Yes, if triangle B had a height of 2\,\text{cm}2cm2, start text, c, m, end text, it would have a base of 1.28\,\text{cm}1.28cm1, point, 28, start text, c, m, end text.
Hint #77 / 7
The following could be the height and base of triangle B:
Height: 2.75\text{ cm}2.75 cm2, point, 75, start text, space, c, m, end text
Base: 1.76\text{ cm}1.76 cm1, point, 76, start text, space, c, m, end text
Height: 1.25\text{ cm}1.25 cm1, point, 25, start text, space, c, m, end text
Base: 0.8\text{ cm}0.8 cm0, point, 8, start text, space, c, m, end text
Height: 2\text{ cm}2 cm2, start text, space, c, m, end text
Base: 1.28\text{ cm}1.28 cm1, point, 28, start text, space, c, m, end text
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