Question

Suki says the area of the triangle is 12 cm². Emilia says the area of the triangle is 10 cm². Find the area of the triangle and explain any errors the girls might have made.

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Answer 1

Let’s call the base of the triangle b and its height h. The area of a triangle is given by the formula A = 1/2 * b * h.

If Suki says that the area of the triangle is 12 cm², then we can write:

12 = 1/2 * b * h

Similarly, if Emilia says that the area of the triangle is 10 cm², then we can write:

10 = 1/2 * b * h

We can solve for one of the variables in terms of the other by dividing both sides of each equation by 1/2:

b * h = 24

b * h = 20

Now we have two equations with two variables. We can solve for one variable in terms of the other by dividing both sides of one equation by the other:

(b * h) / (b * h) = 24 / 20

1 = 6/5

This is a contradiction, so there is no solution that satisfies both equations.

Explanation: