Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6.
Practice Set 1.1 | Q 1 | Page 5
Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.
Let the base, height, and area of the first triangle be b1, h1, and A1 respectively. Let the base, height and area of the second triangle be b2, h2, and A2 respectively.
b1 = 9, h1 = 5, b2 = 10 and h2 = 6.
The ratio of areas of two triangles is equal to the ratio of the products of their bases and corresponding heights.
(A1)/(A2) = (b_1 × h1)/(b2 × h2)
∴ (A1)/(A2) = (9 × 5)/(10 × 6)
∴ (A1)/(A2) = 3/4
The ratio of the areas of the triangles is 3: 4.
Solution 2:-
The area of a triangle is given by the formula:
Area = (1/2) * base * height
Using this formula, we can find the areas of the two triangles:
Area of the first triangle = (1/2) * 9 * 5 = 22.5 Area of the second triangle = (1/2) * 10 * 6 = 30
To find the ratio of the areas of these two triangles, we divide the area of the second triangle by the area of the first triangle:
Ratio of areas = Area of the second triangle / Area of the first triangle = 30 / 22.5 = 4/3
Therefore, the ratio of areas of the two triangles is 4:3.
Chapter 1. Similarity- Practice Set 1.1 – Page 5
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