Question

Construct a ∆ABC in which BC = 5.6 cm, ∠B = 30° and (AB - AC) = 3 cm. Measure AB and AC. Justify your construction.​

Answer 1

$\huge\underline{\underline{\texttt{{Question:}}}}$

• Construct a ∆ABC in which BC = 5.6 cm, ∠B = 30° and (AB - AC) = 3 cm. Measure AB and AC. Justify your construction.

$\huge\underline{\underline{\texttt{{Solution:}}}}$

$\huge\bold\red{steps \: of \: construction : }$

1. Draw BC = 5.6 cm.
2. Construct ∠CBX = 30°
3. Along BX, set off BD = 3 cm.
4. Join CD.
5. Draw the right bisector of CD, meeting BD produced at A.
6. Join AC.

$\small\bold\pink{then \: \triangle \: abc \: is \: required \: triangle.}$

$\huge\bold\red{verification : }$

$\small\bold{on \: measuring \: we \: find \: that \: ab = 6.1 \: cm \: and \: ac = 3.1 \: cm.}$

$\small\bold{\therefore(ab - ac) = (6.1 - 3.1)cm = 3cm.}$

$\huge\bold\red{justification: }$

Since A lies on the perpendicular bisector of CD, we have AD = AC.

$\small\bold{now \: bd = 3cm \: \implies \: ab - ad = 3cm} \\ \implies\small\bold{ab - ac = 3cm} \: \: \: (\therefore \: ad = ac).$

$\star{\boxed{\sf{hence \: \triangle \: abc \: is \: the \: required \: triangle.}}}$

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