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( Brain + 100 points ) A triangle has an area of 30 cm squared. What might the base and height be? Give 3 examples.

Sagot :

loneguy

[tex]\text{The base and height have to be factors of 60, since}\\\\~~~~~~~~\text{Area}= \dfrac{1}{2} \times \text{Base} \times \text{Height}\\\\\implies 30 = \dfrac 12 \times \text{Base} \times \text{Height}\\\\\implies \text{Base} \times \text{Height}= 60[/tex]

[tex]\textbf{Example 1:}\\\\\text{Height} = 6~ cm \\\\\text{Base} = 10~ cm\\\\\text{Area} = \dfrac 12 \times 6 \times 10 = 30~ cm^2\\\\\textbf{Example 2:}\\\\\text{Height} = 5~ cm\\\\\text{Base} = 12~ cm\\\\\text{Area} = \dfrac 12 \times 12 \times 5 = 30~ cm^2\\\\\textbf{Example 3:}\\\\\text{Height} =4~ cm\\\\\text{Base} = ~15 ~cm\\\\\text{Area} = \dfrac 12 \times 15 \times 4 = 30~ cm^2[/tex]

Let's see

Base be B

Height be H

So

  • 1/2BH=30
  • BH=2(30)
  • BH=60

The ppossible values are

  • B=6,H=10
  • H=6,B=10
  • H=3,B=20
  • B=3,H=20
  • B=2,H=30
  • H=2,B=30
  • H=1,B=60
  • B=1,H=60
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