Question

seg AB ⊥ seg BC and seg DC ⊥ seg BC. If AB =3cm & CD=4cm, then find A(∆ ABC)/A(∆ DCB).​

Answer 1

The value of A(∆ ABC)/A(∆ DCB) = 3/4.

Given:

Line seg AB ⊥ Line seg BC  

Line seg DC ⊥ Line seg BC

AB = 3 cm and CD = 4 cm

To find:

A(∆ ABC)/A(∆ DCB)

Solution:

Formula used:

Area of a triangle = (1/2) × base × height  

Here we have

Line seg AB ⊥ Line seg BC  

Line seg DC ⊥ Line seg BC

From Δ ABC

Area of Δ ABC = (1/2)×BC × AB

From Δ BCD

Area of Δ BCD = (1/2) BC × DC

=> A(∆ ABC)/A(∆ DCB)

= $\frac{(1/2) \times BC \times AB}{(1/2) \times BC \times DC}$

= $\frac{ AB}{ DC}$  

From the given data,

AB = 3 cm and CD = 4 cm

= $\frac{ AB}{ DC} = \frac{3}{4}$  

Therefore,

The value of A(∆ ABC)/A(∆ DCB) = 3/4.

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