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Question

A triangle and a parallelogram have the same base and same base and same area. If the sides of the triangle are $$26$$ cm, $$28$$ cm, and $$30$$ cm and the parallelogram stands on the base $$28$$ cm, find the height of the parallelogram.


A
8 cm
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B
10 cm
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C
12 cm
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D
14 cm
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Solution

The correct option is C $$12$$ cm
Area of triangle $$=\sqrt{s(s-a)(s-b)(s-c)}$$

      $$s=\dfrac{a+b+c}{2}$$

$$\Rightarrow s=\dfrac{26+28+30}{2}\Rightarrow s=42$$

Area of triangle$$=\sqrt{42\times16\times14\times12}$$

                          $$=336$$

Area of parallelogram = Area of triangle

                    $$\Rightarrow h \times b =336$$

                               $$h=\dfrac{336}{28}$$

                        $$\Rightarrow h=12$$cm

Mathematics

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