Without using a set square or protractor, construct a rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Find the point R on AD such that RB = RC. What is the length of AR?
Without using a set square or protractor, construct a rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Find the point R on AD such that RB = RC. What is the length of AR?
The correct option is C 1.2 cm
STEP I Draw AB = 4cm
STEP II With B as center and radius = 4cm draw an arc.
STEP III With A as centre and radius = 5cm draw an arc cutting arc drawn in step II at C.
STEP IV With C and A as centers draw arcs of radii = 4cm cutting each other at D.
STEP V Join BC, CD and AD to get the rhombus ABCD.
By measuring ∠ ABC with the protractor, we find that ∠ ABC = 78∘ .
Draw perpendicular bisector of BC. Suppose it cuts AD at R.
Since any point on the perpendicular bisector of BC is equidistant from B and C. So, R is equidistant from B and C.
By measuring AR, we find that AR = 1.2 cm
1.2 cm
STEP I Draw AB = 4cm
STEP II With B as center and radius = 4cm draw an arc.
STEP III With A as centre and radius = 5cm draw an arc cutting arc drawn in step II at C.
STEP IV With C and A as centers draw arcs of radii = 4cm cutting each other at D.
STEP V Join BC, CD and AD to get the rhombus ABCD.
By measuring ∠ ABC with the protractor, we find that ∠ ABC = 78∘ .
Draw perpendicular bisector of BC. Suppose it cuts AD at R.
Since any point on the perpendicular bisector of BC is equidistant from B and C. So, R is equidistant from B and C.
By measuring AR, we find that AR = 1.2 cm
