In ∆ABC, B - D - C and BD = 7, BC = 20 then Find following ratio. A(∆ ABD)/A(∆ ADC)

Answer:_ 

Step 1: BC = BD + DC …[B – D – C]

This step involves adding the lengths of two line segments BD and DC to find the length of BC. The statement [B – D – C] is a shorthand way of indicating that points B, D, and C are collinear, or lie on the same line segment.

Step 2: DC = BC – BD

This step involves subtracting the length of BD from BC to find the length of DC. This is possible because we know that BC = BD + DC (from Step 1), so rearranging the equation gives DC = BC – BD.

Step 3: DC = 20 – 7

This step substitutes the values given in the problem for BC and BD, which are 20 and 7, respectively. This gives us the value of DC as 13.

Step 4: Ratio of areas of two triangles

This step involves applying the formula for the ratio of the areas of two triangles to find the ratio of the areas of ∆ABD and ∆ADC. The formula states that the ratio of the areas of two triangles is equal to the ratio of the products of their bases and corresponding heights.

Step 5: A(∆ABD)/A(∆ADC) = (1/2 * AX * BD)/(1/2 * AX * DC)

This step applies the formula from Step 4 to the triangles ∆ABD and ∆ADC. We know that the base of both triangles is AX, and their corresponding heights are BD and DC, respectively.

Step 6: A(∆ABD)/A(∆ADC) = BD/DC

This step simplifies the expression obtained in Step 5 by cancelling the common factor of (1/2 * AX) from both the numerator and denominator. This gives us the ratio of BD to DC.

Step 7: A(∆ABD)/A(∆ADC) = 7/13

This step substitutes the given values for BD and DC into the expression obtained in Step 6, which gives us the ratio of the areas of the triangles ∆ABD and ∆ADC as 7/13.