Question

in a triangleMN is parallel to AB,BC equal to 7.5 CM, AMequal to 4 cm and MC equal to 2 cm,
find the length of BN

Answer 1

✬ BN = 5 cm ✬

Step-by-step explanation:

Given:

• A ∆ABC in which (See attachment)
• MN || AB
• BC = 7.5 cm , AM = 4 cm & MC = 2 cm.

To Find:

• What is the length of BN

Solution: Let the length of BN be x cm. Therefore, In ∆ABC , MN || AB

$∴ \frac{MC}{AC} = \frac{NC}{BC}$

[By Thales' Theorem: This theorem states that if a line is drawn parallel to one side of a triangle to the intersect the other sides in distinct points then the two sides are divided in the same ratio.]

$\implies \frac{MC}{AC} = \frac{NC}{BC} \\ \\ \implies \frac{MC}{AM + MC} = \frac{NC}{BC} \\ \\ \implies \frac{2}{4 + 2} = \frac{x}{7.5} \\ \\ \implies \frac{2}{6} = \frac{x}{7.5} \\ \\ \implies x = ( \frac{2 \times 7.5}{6}) \\ \\ \implies x = \frac{15}{6} \\ \\ \implies NC = x = 2.5 cm$

So,

➮ BN = ( BC – NC)

➮ BN = (7.5 – 2.5) = 5 cm

Hence, the length of BN is 5 cm.

Answer 2

✬ BN = 5 cm ✬

Step-by-step explanation:

Given:

A ∆ABC in which (See attachment)

MN || AB

BC = 7.5 cm , AM = 4 cm & MC = 2 cm.

To Find:

What is the length of BN

Solution: Let the length of BN be x cm. Therefore, In ∆ABC , MN || AB

=ACMC

= BCNC

[By Thales' Theorem: This theorem states that if a line is drawn parallel to one side of a triangle to the intersect the other sides in distinct points then the two sides are divided in the same ratio.]

⟹ ACMC

= BCNC

⟹ AM+MCMC

= BCNC

⟹ 4+22

= 7.5x

⟹ 62

= 7.5x

⟹x=( 62×7.5 )

⟹x= 6

15

⟹NC=x=2.5cm

So,

➮ BN = ( BC – NC)

➮ BN = (7.5 – 2.5) = 5 cm

Hence, the length of BN is 5 cm.