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Question
ΔAMT∼ΔAHE, construct Δ AMT such that MA = 6.3 cm, ∠MAT=120°, AT = 4.9 cm and `"MA"/"HA"=7/5`, then construct ΔAHE.
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Solution
Δ AMT and Δ AHE are give
⇒ `("MA")/("HA")= ("AT")/("AE") =("TM")/("EH")=7/5`
⇒ `("MA")/("HA")=7/5 ⇒ 6.3/"HA" =7/5`
⇒ `"HA" =(6.3xx5)/7`
⇒ HA = 4.5cm
Similarly, `"AT"/"AE" =7/5`
⇒ `4.9/"AE" =7/5 ⇒"AE" =(4.9xx5)/7⇒"AE"=3.5`cm
Given triangle Required triangle
Steps of Constructing the required triangle:
1. Draw a line segment of some length HP and mark an arc of 4.5cm(as calculated above) and name it as A.
2. At vertex A, make an angle of 120°
3. Mark an arc of 3.5cm (as calculated above) on AT’ and name it E.
4. Join HE.
5. Δ AHE is the required triangle.
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