The height of a triangle is three-fifth its base. If the height is increased by 4 cm and the base is decreased by 2 cm, the area of the triangle remains the same. Find the base of the triangle.

20/14

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30/14

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40/14

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50/14

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Solution

The correct option is C
40/14

Let the base of the triangle be $x$ .

Then, its height = $\frac{3 x}{5}$

If height is increased by 4 cm, then new height $= \frac{3 x}{5} + 4$

New base = $x - 2$

Area of triangle = $\frac{1}{2} \times base \times height$

Since the area remains the same, $x \times \frac{3 x}{5} = (\frac{3 x}{5} + 4) \times (x - 2)$

$\frac{3 x^{2}}{5} = \frac{3 x^{2}}{5} + 4 x - \frac{6 x}{5} - 8$

$x = \frac{40}{14}$ = $\frac{20}{7}$ cm

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The height of a triangle is three-fifth its base. If the height is increased by 4 cm and the base is decreased by 2 cm, the area of the triangle remains the same. Find the base of the triangle.

The correct option is C 40/14 Let the base of the triangle be x. Then, its height = 3x5 If height is increased by 4 cm, then new height =3x5+4 New base = x−2 Area of triangle = 12×base×height Since the area remains the same, x×3x5=(3x5+4)×(x−2) 3x25 = 3x25+4x−6x5−8 x=4014 = 207 cm