Question : Given that the ratio of the altitude of two triangles is 4 : 5, the ratio of their areas is 3 : 2, the ratio of their corresponding bases is:
Option 1: 8 : 15
Option 2: 15 : 8
Option 3: 5 : 8
Option 4: 8 : 5

Question

Question : Given that the ratio of the altitude of two triangles is 4 : 5, the ratio of their areas is 3 : 2, the ratio of their corresponding bases is:

Option 1: 8 : 15

Option 2: 15 : 8

Option 3: 5 : 8

Option 4: 8 : 5

Team Careers360 · Accepted Answer

Correct Answer: 15 : 8

Solution : The area of a triangle $=\frac{1}{2} imes ext{base} imes ext{height}$
Given that the ratio of the altitudes of two triangles is 4 : 5 and the ratio of their areas is 3 : 2.
$\frac{ ext{Area of Triangle 1}}{ ext{Area of Triangle 2}} = \frac{ ext{Base of Triangle 1} imes ext{Height of Triangle 1}}{ ext{Base of Triangle 2} imes ext{Height of Triangle 2}}$
$⇒\frac{3}{2} = \frac{ ext{Base of Triangle 1} imes 4}{ ext{Base of Triangle 2} imes 5}$
$⇒\frac{ ext{Base of Triangle 1}}{ ext{Base of Triangle 2}}=\frac{3 imes 5}{2 imes 4}=\frac{15}{8}$
Hence, the correct answer is 15 : 8

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Question : Given that the ratio of the altitude of two triangles is 4 : 5, the ratio of their areas is 3 : 2, the ratio of their corresponding bases is:Option 1: 8 : 15Option 2: 15 : 8Option 3: 5 : 8Option 4: 8 : 5

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Question : Given that the ratio of the altitude of two triangles is 4 : 5, the ratio of their areas is 3 : 2, the ratio of their corresponding bases is:
Option 1: 8 : 15
Option 2: 15 : 8
Option 3: 5 : 8
Option 4: 8 : 5