Question

the base and height are given in ratio 3:4 and it's area is 96 square cm find. it's Base and height

Answer 1

$let \: the \: common \: ratio \: be \: x \\ base = 3x \: height = 4x \\ area \: of \: a \: triangle = \frac{1}{2} \times base \times height \\ 96 = \frac{1}{2} \times 3x \times 4x \\ 96 = \frac{1}{2} \times 12x { }^{2} \\ 96 = \frac{12}{2}x { }^{2} \\ x { }^{2} = \frac{96 \times 2}{12} \\ x { }^{2} = 36 \\ x = \sqrt{36} \\ x = 6 \\ then \: \\ base = 3x = 3 \times 6 = 18 cm\\ height = 4x = 4 \times 6 = 24cm$
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Answer 2

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Question

The base and height of at triangle are in the ratio 3:4 and its area is 96 sq.m . find its base and height

Answer: base = 3×4 = 12cm and height = 4×4 = 16 cm

Solution

Let the base be 3x

Let the height be 4x

Area of triangle, A = ½ × base × altitude = 96 m²

96 = ½ × base × ¼ base

96 = 6x²

x² = 16 or x = 4

base = 3×4 = 12cm and

height = 4×4 = 16 cm

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