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the height of a triangle is 10 centimeters more than its base. if the area of the triangle is 100 square centimeters, find its base and height.

User ShmulikA
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1 Answer

2 votes

Answer:

The base is 10cm and the height is 20cm.

Explanation:

Let's start with the base. We don't know what it is. Because I do not like using b as a variable, let's use x.

x = base

Huh, we don't know the height either. But we know it is 10cm longer than the base.

h = x + 10

Also we know the area of the triangle, 100cm^2.

Use the area formula for a triangle:

A = 1/2bh

Fill in what we know.

100 = 1/2(x)(x + 10)

Times by 2 to just rid ourselves of fractions.

200 = x(x + 10)

Use distributive property.

200 = x^2 + 10x

subtract 200

0 = x^2 + 10x - 200

Factor.

0 = (x + 20)(x - 10)

Use Zero Product Property (this just means set each factor equal to zero)

x + 20 = 0 and x - 10 = 0

for x + 20 = 0,

subtract 20

x = -20

We'll trash this answer because lengths cannot be negative.

For the second equation, x - 10 = 0

add 10

x = 10

Remember x is the base. So the base is 10cm.

The height is 10cm longer, so the height is 20cm.

Check: if

base = 10

height = 20

Area = 1/2bh

Area = 1/2(10)(20)

Area = 100 check!

The base is 10cm and the height is 20cm.

User Ivallesp
by
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