Height of a triangle is decreased by 30 percent. If the net increase i

1.	Height of a triangle is decreased by 30 percent. If the net increase in the area of the triangle is of 5 percent, then by how much percentage the base of triangle is increased?1. 25 percent2. 66.67 percent3. 33.33 percent4. 50 percent
Answer» Correct Answer - Option 4 : 50 percent Given: The height of the triangle decreased = 30% Formula used: The area of the triangle = (1/2) × (b × h) (Where b = The base of the triangle, h = The height of the triangle) Calculation: Let us assume the base of the triangle increased by X% and the area of the triangle is A ⇒ The area of the triangle = A = bh/2 ⇒ \(b\ = {2A\over h}\) ----(1) ⇒ When the area of the triangle increase by 5% ⇒ \({A\ \times 1.05}\ = {(h\ \times 0.7)\ \times b\over2}\) ⇒ b = \(b\ =\ {2.1A\over 0.7h}\ =\ {3A\over h}\) ----(2) ⇒ The increment in the base of the triangle = \({({3A\over h}\ - {2A\over h})\over {2A\over h}} \times 100\) = 50% ∴ The required result will be 50%.

Height of a triangle is decreased by 30 percent. If the net increase in the area of the triangle is of 5 percent, then by how much percentage the base of triangle is increased?1. 25 percent2. 66.67 percent3. 33.33 percent4. 50 percent

Answer» Correct Answer - Option 4 : 50 percent

Given:

The height of the triangle decreased = 30%

Formula used:

The area of the triangle = (1/2) × (b × h) (Where b = The base of the triangle, h = The height of the triangle)

Calculation:

Let us assume the base of the triangle increased by X% and the area of the triangle is A

⇒ The area of the triangle = A = bh/2

⇒ \(b\ = {2A\over h}\) ----(1)

⇒ When the area of the triangle increase by 5%

⇒ \({A\ \times 1.05}\ = {(h\ \times 0.7)\ \times b\over2}\)

⇒ b = \(b\ =\ {2.1A\over 0.7h}\ =\ {3A\over h}\) ----(2)

⇒ The increment in the base of the triangle = \({({3A\over h}\ - {2A\over h})\over {2A\over h}} \times 100\) = 50%

∴ The required result will be 50%.