In the given figure, ∠ABC = ∠DCB = 90° AB = 6, DC = 8 then
Problem Set 1 | Q 4 | Page 27
In the given figure, ∠ABC = ∠DCB = 90° AB = 6, DC = 8 then [frac{A left( ∆ ABC right)}{A left( ∆ DCB right)} = ?]
Solution
Given:
∠ABC = ∠DCB = 90°
AB = 6
DC = 8
[Now, frac{A left( ∆ ABC right)}{A left( ∆ DCB right)} = frac{frac{1}{2} times AB times BC}{frac{1}{2} times DC times BC}]
[ = frac{6}{8}]
[ = frac{3}{4}]
Answer:_ Given:
- ∠ABC = ∠DCB = 90°
- AB = 6
- DC = 8
To find: Ratio of areas of triangles ∆ABC and ∆DCB
Solution: The area of a triangle is given by the formula A = 1/2 × base × height. Since the two triangles ∆ABC and ∆DCB share a common height (BC), the ratio of their areas can be found by comparing their bases.
Using the given information, we can see that:
- The base of ∆ABC is AB = 6.
- The base of ∆DCB is DC = 8.
Therefore, the ratio of the areas of the two triangles is:
A(∆ABC) / A(∆DCB) = (1/2 × AB × BC) / (1/2 × DC × BC) = AB / DC = 6 / 8 = 3 / 4
Hence, the ratio of the areas of the two triangles ∆ABC and ∆DCB is 3:4.
Problem Set 1 | Q 4 | Page 27
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