Question

helene was given the following enlargement of a triangle.
image of two triangles: small blue triangle with legs 10 cm, 12 cm, hypotenuse 13 cm; large red triangle with base 36 cm, sides a and b
figures not drawn to scale.
what are the lengths of sides a and b?
○ a = 30 cm, b = 39 cm
○ a = 30 cm, b = 48 cm
○ a = 20 cm, b = 26 cm
○ a = 20 cm, b = 33 cm

Explanation:

Step1: Find the scale factor

The original base is \( 12 \, \text{cm} \), and the enlarged base is \( 36 \, \text{cm} \). The scale factor \( k \) is calculated as \( k=\frac{36}{12}=3 \).

Step2: Calculate length of \( A \)

The original height is \( 10 \, \text{cm} \). Using the scale factor, the length of \( A \) (enlarged height) is \( 10\times3 = 30 \, \text{cm} \).

Step3: Calculate length of \( B \)

The original hypotenuse is \( 13 \, \text{cm} \). Using the scale factor, the length of \( B \) (enlarged hypotenuse) is \( 13\times3 = 39 \, \text{cm} \).

Answer:

A. \( A = 30 \, \text{cm}, B = 39 \, \text{cm} \)