Question

In the given figure area of square BCFG is 64 $c{m}^2$ and is 4 times the area of ABGH .If the area of rectangle ABGH is equal to that of CDEF then find perimeter of ADEH.

• A. 40 cm
• B. 20 cm
• C. 16 cm
• D. 10 cm

Answer 1

The correct option is A 40 cm

Area of square BCFG = $sid{e}^2$ = 64 $c{m}^2$
= $B{C}^2$ = 64 $c{m}^2$
= BC = $\sqrt{6}4$ = 8 cm
Hence BC=CF=FG=BG = 8cm
Side of square = 8 cm = BG= AH
According to condition
4$\times$Area of ABGH = area of BCFG
Area of ABGH = $\frac{64}{4}$ = 16 $c{m}^2$
Length$\times$Breadth = 16 $c{m}^2$
AH $\times$breadth = 16 $c{m}^2$
Breadth = $\frac{16}{8}$ = 2 cm = AB= CD
For ADEH ,AD = AB+BC+CD = 2 + 8 + 2 = 12 cm
AH = 8 cm
Perimeter of ADEH
= 2$\times$(length + breadth)
= 2$\times$(AD + AH)
= 2$\times$(12 + 8 )
= 40 cm