Question
Download Solution PDFTwo similar triangles of ΔXYZ and ΔLMN. If area of (ΔXYZ) = 16 cm2, area of (ΔLMN) = 25 cm2 and YZ = 2.4 cm, then the measure of MN is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Area of ΔXYZ = 16 cm2
Area of ΔLMN = 25 cm2
YZ = 2.4 cm
Formula Used:
\( \frac{\text{Area of ΔXYZ}}{\text{Area of ΔLMN}} = \left( \frac{\text{YZ}}{\text{MN}} \right)^2\)
Calculation:
\(\frac{16}{25} = \left( \frac{2.4}{\text{MN}} \right)^2\)
⇒ \(\sqrt{\frac{16}{25}} = \frac{2.4}{\text{MN}}\)
⇒ \( \frac{4}{5} = \frac{2.4}{\text{MN}}\)
⇒ \( \text{MN} = \frac{2.4 \times 5}{4}\)
⇒ MN = 3 cm
Therefore, the measure of MN is 3 cm.
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