Find the dimensions of the square whose area is equal to area of rectangle (with dimensions 5 cm × 4 cm) [Use construction]
Find the dimensions of the square whose area is equal to area of rectangle (with dimensions 5 cm × 4 cm) [Use construction]
The correct option is D 4.5
Method of Construction:
(i) Let us draw a rectangle ABCD at first, the length of which is AB = 5 cm and the breadth BC = 4 cm.
(ii) DC is extended to Y. The part CR is cut off from CY, such that CR = 4 cm.
(iii) Let us draw a perpendicular bisector PQ of DR. Let PQ intersect DR at M.
(iv) Let us now draw a semi circle with centre at M and radius equal to DM or MR.
(v) Let us draw a perpendicular CG on CR at the point C. Let CG intersect the semicircle at G.
(vi) Let us now draw two arcs simultaneously in the same side of GC by taking centres at C and G respectively and with radius equal to CG.
(vii) Let us draw another arc with centre at E and radius equal to CG, which intersects the previous arc at the point F.
(viii) Join E, F and G, F.
CEFG is the required square.
Area of rectangle DCAB = Area of square GFCE
Dimensions of Square GFCE :
Each side of Square GFCE measure to b 4.5 cm (approx )
4.5
Method of Construction:
(i) Let us draw a rectangle ABCD at first, the length of which is AB = 5 cm and the breadth BC = 4 cm.
(ii) DC is extended to Y. The part CR is cut off from CY, such that CR = 4 cm.
(iii) Let us draw a perpendicular bisector PQ of DR. Let PQ intersect DR at M.
(iv) Let us now draw a semi circle with centre at M and radius equal to DM or MR.
(v) Let us draw a perpendicular CG on CR at the point C. Let CG intersect the semicircle at G.
(vi) Let us now draw two arcs simultaneously in the same side of GC by taking centres at C and G respectively and with radius equal to CG.
(vii) Let us draw another arc with centre at E and radius equal to CG, which intersects the previous arc at the point F.
(viii) Join E, F and G, F.
CEFG is the required square.
Area of rectangle DCAB = Area of square GFCE
Dimensions of Square GFCE :
Each side of Square GFCE measure to b 4.5 cm (approx )
