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The triangle PQR is the image of the triangle DEF under an enlargement - Leaving Cert Mathematics - Question b - 2021
Question b
The triangle PQR is the image of the triangle DEF under an enlargement. (The diagram is not drawn to scale.) The scale factor of the enlargement, k_s, is 2.5. |EF| =... show full transcript
Worked Solution & Example Answer:The triangle PQR is the image of the triangle DEF under an enlargement - Leaving Cert Mathematics - Question b - 2021
Step 1
Use the scale factor to find |QR|.
Answer
To find the length |QR|, we use the scale factor of the enlargement, which is given as k_s = 2.5. The corresponding length in triangle DEF is |EF|, which measures 3 cm. The formula for finding the new length after enlargement is:
Substituting the known values:
Step 2
The area of triangle PQR is 18.75 cm². Find the area of triangle DEF.
Answer
To find the area of triangle DEF, we need to account for the fact that the area of a triangle scales with the square of the scale factor. Using the area of triangle PQR, we use the following relationship:
ext{Area}_{DEF} = rac{ ext{Area}_{PQR}}{k_s^2}
First, calculate the square of the scale factor:
Now plug in the area of triangle PQR:
ext{Area}_{DEF} = rac{18.75}{6.25} = 3 ext{ cm}^2