Question

In triangle Abc Ab :Bc 3:4 Bc:Ac=5:4. (a) If Ab=30cm what is the length of bc ? (b) If bc =20cm what is the length of Ab and Ac. (c) what is Ab:Bc:Ac?​

Answer 1

Given:

In a triangle ABC,

AB : BC = 3 : 4 and BC : AC = 5 : 4

To find:

a). If AB = 30 cm then length of BC.

b). If BC = 20 cm then length of AB and BC.

c). AB : BC : AC

Solution:

a). Since, AB : BC = 3 : 4

   Or $\frac{AB}{BC}=\frac{3}{4}$

   If, AB = 30 cm

   $\frac{30}{BC}= \frac{3}{4}$

   BC = $\frac{30\times 4}{3}$

   BC = 40 cm

b). Since, $\frac{BC}{AC}=\frac{5}{4}$

    If BC = 20 cm,

    $\frac{20}{AC}=\frac{5}{4}$

    AC = 16 cm

c). Since, $\frac{AB}{BC}=\frac{3}{4}$

   Therefore, AB = $\frac{3}{4}(BC)$

   Since, $\frac{BC}{AC}=\frac{5}{4}$

   AC = $\frac{4}{5}(BC)$

   Now, AB : BC : AC = $\frac{3}{4}(BC):BC:\frac{4}{5}(BC)$

                                   = $\frac{3}{4}:1:\frac{4}{5}$