Question

If area of $△$ABC and $△$ADC are 30 $c{m}^2$ and 40 $c{m}^2$ respectively. If AC = 10 cm, then find lengths of BE and DF.

• A. 3 cm, 4 cm
• B. 4 cm, 3 cm
• C. 6 cm, 8 cm
• D. 8 cm, 6 cm

Answer 1

The correct option is C 6 cm, 8 cm

Area of $△$ABC = $\frac{1}{2}$$\times$base$\times$height
30 = $\frac{1}{2}$$\times$AC$\times$BE
BE = $\frac{30\times 2}{AC}$ = $\frac{30\times 2}{10}$ = 3$\times$2 = 6 cm

Similarly
Area of $△$ADC = $\frac{1}{2}$$\times$base$\times$height
40 = $\frac{1}{2}$$\times$AC$\times$DF
DF = $\frac{40\times 2}{AC}$ = $\frac{40\times 2}{10}$ = 4$\times$2 = 8 cm