Question

in the adjoining diagram, abc is a right-angle triangle and bdef is a square. if ab = 8 cm, bc = 6 cm, find the length of each side of the square.

Hints : Area of triangle ADE+ area of triangle EFC+ area of square BDEF= area of triangle ABC. ​

Answer 1

Step-by-step explanation:

here, AB =8cm

BC =6cm

AD =(8-x)cm

DE= x cm

EF= x cm

CF =(6-x) cm

Area of ∆ABC = Area of ∆ADE + Area of ∆ EFC + Area of square BDEF

½ × BC× AB = ½ × ED × AD + ½ × CF × EF + (side)²

½× 6 × 8 = ½ × (x)×(8-x) + ½ (6-x) × (x) + x²

24 = x(8-x)/2 + x(6-x)/2 + x²

24× 2= 8x - x² + 6x - x² + 2x²

48 = 14x -2x²+2x²

48= 14x

x= 48/14

x= 24/7

x= 3.43cm

length of each side of a square is 3.43cm.