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The base of a triangle is 3 cm longer than its
corresponding height. If the area is 44 cm?,
find the length of its base.

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Given : The base of a triangle is 3 cm longer than its corresponding height. If the area is 44 cm? Find the length of its base.

Solution : According to the question here we are given that the base is 3 cm longer than height. So,

Let's assume the height to be a

Now, as the base is 3 cm longer than the height. So,

the base is a - 3

As we know that Area = ½ × base × height

Hence, putting the values we get

  • 44 = ½ × a + 3 × a

  • 44 = ½ × a² - 3a

  • 44 × 2 = a² - 3a

  • 88 = a² - 3a

  • a² - 3a - 88 = 0

  • (a + 11)(a - 8) = 0

As per the quadratic equations we will get two options the positive will be accepted whereas the negative is rejected

1st equation :

a - 11 = 0

  • a = -11

2nd equation :

a - 8 = 0

  • a = 8

As we know the situation so we get a = 8 as the answer

Base = a + 3 = 8 + 3 = 11 cm

HENCE, the required answer is 11 cm

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