Question

*In a triangle, base is twice its height. What is the length of base if the area of triangle is 64 sq cm?*

1️⃣ 6 cm
2️⃣ 8 cm
3️⃣ 16 cm
4️⃣ 4 cm​

Answer 1

Given : In a triangle, base is twice it's height. Area of the triangle is 64cm².

To Find : Length of the base.

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Let

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• Height of the triangle = k

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Base of the triangle is twice it's height.

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So,

• Base of the triangle = 2k

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It is given that : Area of the triangle is 64cm².

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As we know that :

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$</p><p>\underline{\boxed{\sf\purple{\bigstar \: area \: of \: a \: triangle \: = \frac{1}{2} \times b \times h }}}$

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Where

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• b denotes base of the triangle.
• h denotes height of the triangle.

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Put the values in the formula -

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$\sf:\implies \: area \: of \: the \: triangle \: = \dfrac{1}{2} \times b \times h \\ \\ \\ \sf:\implies \: 64 = \frac{1}{2} \times 2k \times k \\ \\ \\ \sf:\implies \: 64 = \frac{\cancel2k {}^{2} }{\cancel{2} } \\ \\ \\ \sf:\implies \: 64 = {k}^{2} \\ \\ \\ \sf:\implies \: k = \sqrt{64} \\ \\ \\ \sf:\implies \: k = \underline{\boxed{\sf\purple{8cm}}}\bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: base \: of \: the \: triangle = 2k = 2(8) = \bold{16cm}}}$