The height of a triangle is 2 times the base. The area is 25 square inches. Find the base.

Question

I need help on this word problem. thanks

Answer 1

Hi Biana, start with the formula for the area of a triangle, 1/2 * B(ase) * H(eight) = Area

 

If we let B = base, then 2B = height, since the height is 2 times the base. Now replace the values we have in the formula:

 

1/2 * B * 2B = 25

 

1/2 * 2B^2 = 25

 

Multiply both sides by 2 to remove the fraction gives:

 

2B^2 = 50

 

Divide both sides by 2 giving:

 

B^2 = 25

 

The base, B, is the square root of 25, which is 5.

 

The height of the triangle is equal to two times the base, or 10.

 

Check:

 

1/2 * 5 * 10 = 25

 

1/2 * 50 = 25

 

25 = 25, values check.

 

Questions?

Answer 2

Equations needed:   Area of a triangle = 1/2 * b * h

 

Givens: h = 2*b  A = 25 square inches

 

Substitute givens into the equation:

 

25 = 1/2 * b * 2b 

 

Multiply by 2 on both sides and multiply out the right side.

 

50 = 2b^2

 

Divide by 2 on both sides:

 

25 = b^2 

 

Take the square root of both sides.

 

5 = b

 

Base = 5 inches

 

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Jeff Negus

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