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The base of the triangle is increased by 40%. What can be the maximum percentage increase in the length of the height so that the increase in area is restricted to a maximum of 60% ?
- A14.95%
- B14.98%
- C14.28%
- D14.45%
Answer not set
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0
CCommunity
14.28%
0
CCommunity
Consider the provided information.
Let the height of the triangle is h and base is b.
It is given that height increased by 40%
New height = h + 40% of h
New height =
[Image: https://tex.z-dn.net/?f=h%2B%5Cfrac%7B2%7D%7B5%7Dh%3D%5Cfrac%7B7%7D%7B5%7Dh]
The area of triangle is:
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)]
Let new base be x, then
Thus,
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D(x%5Ctimes%20%5Cfrac%7B7%7D%7B5%7Dh)]
The Area increases by 60%. so, new area,
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)%2B%5Cfrac%7B60%7D%7B100%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20%5Cfrac%7B7%7D%7B5%7Dh)]
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B8%7D%7B5%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)]
Substitute the value of A from above.
[Image: https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B5%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)%3D%5Cfrac%7B1%7D%7B2%7D(x%5Ctimes%20%5Cfrac%7B7%7D%7B5%7Dh)]
[Image: https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B5%7D%5Ctimes%20b%3D%5Cfrac%7B7%7D%7B5%7Dx%5C%5C%5C%5Cx%3D%5Cfrac%7B8%7D%7B7%7Db]
So, base will increase by 1/7th of b=14.28%.
Let the height of the triangle is h and base is b.
It is given that height increased by 40%
New height = h + 40% of h
New height =
[Image: https://tex.z-dn.net/?f=h%2B%5Cfrac%7B2%7D%7B5%7Dh%3D%5Cfrac%7B7%7D%7B5%7Dh]
The area of triangle is:
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)]
Let new base be x, then
Thus,
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D(x%5Ctimes%20%5Cfrac%7B7%7D%7B5%7Dh)]
The Area increases by 60%. so, new area,
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)%2B%5Cfrac%7B60%7D%7B100%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20%5Cfrac%7B7%7D%7B5%7Dh)]
[Image: https://tex.z-dn.net/?f=A%3D%5Cfrac%7B8%7D%7B5%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)]
Substitute the value of A from above.
[Image: https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B5%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D(b%5Ctimes%20h)%3D%5Cfrac%7B1%7D%7B2%7D(x%5Ctimes%20%5Cfrac%7B7%7D%7B5%7Dh)]
[Image: https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B5%7D%5Ctimes%20b%3D%5Cfrac%7B7%7D%7B5%7Dx%5C%5C%5C%5Cx%3D%5Cfrac%7B8%7D%7B7%7Db]
So, base will increase by 1/7th of b=14.28%.