the two triangles below are mathematically similar, the area of triangle a is 50 cm^2, show that the area of triangle B is 8x^2 +8x+2. The adjacent of triangle A is 5x+15. the adjacent of triangle B is 2x^2+7x+3.

Answer 1

Since the two triangles are mathematically similar, the ratio of corresponding sides is equal.

Let the base of triangle A be b, and let the corresponding base of triangle B be y.

Therefore, we have the equation:

\( \frac{b}{y} = \frac{5x+15}{2x^2+7x+3} \)

Since the area of a triangle is given by the formula:

Area = 0.5 * base * height

We can say:

Area A = 0.5 * b * (5x+15) = 50

Area B = 0.5 * y * (2x^2 + 7x + 3)

Since the two triangles are similar, the ratio of the areas is equal to the square of the ratio of the bases:

\( \frac{Area A}{Area B} = \left( \frac{b}{y} \right)^2 \)

Substituting the values:

\( \frac{50}{Area B} = \left( \frac{5x+15}{2x^2+7x+3} \right)^2 \)

\( Area B = \frac{50(2x^2+7x+3)^2}{(5x+15)^2} \)

\( Area B = \frac{50(4x^4 + 28x^3 + 61x^2 + 42x + 9)}{25x^2 + 150x + 225} \)

\( Area B = 8x^2 + 8x + 2 \)

Therefore, the area of triangle B is 8x^2 + 8x + 2.

Answer 2

\( \frac{b}{y} = \frac{5x+15}{2x^2+7x+3} \). what dies that mean

Answer 3

The expression \( \frac{b}{y} = \frac{5x+15}{2x^2+7x+3} \) represents the ratio of the base of triangle A to the base of triangle B.

It means that the ratio of the length of the base of triangle A to the length of the base of triangle B is equal to the ratio of the lengths of the corresponding sides of the triangles.

If two triangles are similar, then the ratio of corresponding sides is constant. In this case, the ratio of the base of triangle A to the base of triangle B is given by \( \frac{5x+15}{2x^2+7x+3} \).

Therefore, this equation helps us determine the relationship between the bases of the two triangles, and we can use this information to find the area of triangle B based on the given area of triangle A.