Given: $\triangle PQR \cong \triangle STU$, QR = 8 cm, TU = 12 cm, and $A(\triangle PQR) = 128 \, \text{cm}^2$.

Find $A(\triangle STU)$.

A. 192 cm$^2$

B. 160 cm$^2$

C. 176 cm$^2$

D. 184 cm$^2$

The area of triangle STU is 192 cm². This is calculated using the fact that areas of similar polygons are proportional to the squares of the ratios of their corresponding sides.

Explanation:

The problem describes two similar triangles, PQR and STU. The ratio of the sides QR/TU is 8/12 or 2/3. The important information is that the areas of similar polygons are proportional to the squares of the ratios of their corresponding sides. In other words, if the ratio of the sides is a/b, the ratio of the areas is a²/b².

In this case, the ratio of the areas of triangles PQR to STU is (2/3)², which simplifies to 4/9. Given that the area of triangle PQR is 128 cm², we can set up the equation (4/9)*A(triangle STU) = 128 cm² to solve for the area of triangle STU. After cross multiplication and simplification, we find A(triangle STU) = 192 cm², which is option (a).

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Given: \(\triangle PQR \cong \triangle STU\), QR = 8 cm, TU = 12 cm, and \(A(\triangle PQR) = 128 \, \text{cm}^2\).Find \(A(\triangle STU)\).A. 192 cm\(^2\)B. 160 cm\(^2\)C. 176 cm\(^2\)D. 184 cm\(^2\)

Answer :

Final answer:

Explanation:

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Other Questions

Given: \(\triangle PQR \cong \triangle STU\), QR = 8 cm, TU = 12 cm, and \(A(\triangle PQR) = 128 \, \text{cm}^2\).

Find \(A(\triangle STU)\).

A. 192 cm\(^2\)

B. 160 cm\(^2\)

C. 176 cm\(^2\)

D. 184 cm\(^2\)