question_answer

Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are \[\frac{3}{4}\] times the corresponding sides of isosceles triangle.

Answer:

Steps of construction-

(i) Draw a line segment \[AB=6\text{ }cm\].

(ii) Draw a perpendicular bisector PQ of AB.

(iii) Draw an arc at a distance 4 cm (from AB) intersecting PQ at C.

(iv) Join CA and CB.

Thus, \[\Delta \text{ }ABC\]is obtained.

(v) Mark D on AB, such that \[AD=\frac{3}{4}AB=\left( \frac{3}{4}\times 6 \right)cm=\frac{9}{2}cm=4.5\,cm\]

(vi) Draw \[DE\parallel BC\], cutting AC at E.

Then, \[\Delta \text{ }ADE\] is the required triangle similar to \[\Delta \text{ }ABC\]such that each side of \[\Delta \text{ }ADE\] is \[\frac{3}{4}\] times the corresponding side of \[\Delta \text{ }ABC\].