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The area of a triangular flag is 90 cm². Its altitude is 2 cm longer than twice its base. Find the length of the altitude and the base

The area of a triangular flag is 90 cm². Its altitude is 2 cm longer than twice its-example-1
User Stowelly
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1 Answer

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Okay, here we have this:

Considering the provided information, we are going to calculate the requested dimensions, so we obtain the following:

According to the information given then we have:

Area=90 cm²

Base=x

Altitude=2+2x

And replacing in the area formula then we have the equation to solve:

Area=(Base*Altitude)/2

90 cm²=(x*(2+2x))/2

90=(2x+2x^2)/2

180=2x+2x^2

2x+2x^2-180=0

2(x-9)(x+10)=0

x-9=0 or x+10=0

x=9 or x=-10

Finally we only consider the value of x positive because the measurements can only be positive, so we finally get

Base=x=9 cm

Altitude=2+2x=2+(2*9)=2+18=20 cm

Finally we obtain that the length of the base is 9cm and the altitude is 20 cm.

User Dan Fletcher
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