Ratio of areas of two triangles with equal heights is 2 : 3. If base of the smaller triangle is 6 cm then what is the corresponding base of the bigger triangle ?
Problem Set 1 | Q 3 | Page 27
Ratio of areas of two triangles with equal heights is 2 : 3. If base of the smaller triangle is 6 cm then what is the corresponding base of the bigger triangle ?
\[\frac{\text{ Area of smaller triangle }}{\text{ Area of bigger triangle }} = \frac{2}{3}\]
\[ \Rightarrow \frac{\frac{1}{2} \times \text{Height of smaller triangle } \times \text{ Base of smaller triangle }}{\frac{1}{2} \times \text{ Height of bigger triangle } \times \text{ Base of bigger triangle }} = \frac{2}{3}\]
\[ \Rightarrow \frac{6}{\text{ Base of bigger triangle }} = \frac{2}{3}\]
\[\Rightarrow \text{ Base of bigger triangle } = \frac{3}{2} \times 6\]
\[ = 9\]
Answer:-
Step 1: Use the formula for the area of a triangle
The first step involves using the formula for the area of a triangle, which states that the area of a triangle is equal to half the product of its base and height. We can write this as:
Area of smaller triangle = (1/2 * height of smaller triangle * base of smaller triangle) Area of bigger triangle = (1/2 * height of bigger triangle * base of bigger triangle)
Step 2: Substitute the expressions for the areas
The second step involves substituting the expressions for the areas of the two triangles from Step 1 into the given ratio of areas, which gives:
Area of smaller triangle/Area of bigger triangle = (2/3)
Substituting the expressions for the areas of the triangles, we get:
(1/2 * height of smaller triangle * base of smaller triangle)/(1/2 * height of bigger triangle * base of bigger triangle) = (2/3)
Step 3: Simplify the expression
The third step involves simplifying the expression obtained in Step 2 by cancelling the common factor of (1/2) and rearranging to solve for the unknown base of the bigger triangle. This gives us:
(Height of smaller triangle/Height of bigger triangle) = (2/3)
Multiplying both sides by the height of the bigger triangle, we get:
Height of smaller triangle = (2/3) * Height of bigger triangle
Substituting this into the expression obtained in Step 2, we get:
(Base of smaller triangle/Base of bigger triangle) = (2/3)
Multiplying both sides by the base of the bigger triangle and simplifying, we get:
Base of bigger triangle = (3/2) * Base of smaller triangle
Step 4: Substitute the given values
The final step involves substituting the given value of the base of the smaller triangle into the expression obtained in Step 3 to find the length of the base of the bigger triangle. This gives us:
Base of bigger triangle = (3/2) * 6
Base of bigger triangle = 9
Problem Set 1 | Q 3 | Page 27
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