Find the dimensions of a square whose area is same as that of an equilateral triangle of dimensions 3 cm. (Use construction)
Find the dimensions of a square whose area is same as that of an equilateral triangle of dimensions 3 cm. (Use construction)
The correct option is C 1.9
i) Draw a rectangle CDEF of area equal to the area of ΔABC
ii) Extend EF to N. Let us cut off the part FG from extended FN equal to CF.
iii) Draw perpendicular bisector of EG which intersects EG at the point O.
iv) Draw a semi circle with centre at O and radius equal to OE and OG.
v) Extend CF in the upward direction, which intersects the semi circle at R.
vi) Draw an arc with centre F, and radius equal to FR along FN, which intersects FN at P.
vii) Now, draw two arcs, one with centre at R and radius equal to RF and another with centre at P and radius equal to RF. Let these two arcs intersect each other at the point Q.
viii) Join P, Q and R, Q. FPQR is the required square with dimensions 1.9 cm.
1.9
i) Draw a rectangle CDEF of area equal to the area of ΔABC
ii) Extend EF to N. Let us cut off the part FG from extended FN equal to CF.
iii) Draw perpendicular bisector of EG which intersects EG at the point O.
iv) Draw a semi circle with centre at O and radius equal to OE and OG.
v) Extend CF in the upward direction, which intersects the semi circle at R.
vi) Draw an arc with centre F, and radius equal to FR along FN, which intersects FN at P.
vii) Now, draw two arcs, one with centre at R and radius equal to RF and another with centre at P and radius equal to RF. Let these two arcs intersect each other at the point Q.
viii) Join P, Q and R, Q. FPQR is the required square with dimensions 1.9 cm.
