Question

# A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are$26cm,28cmand30cm$, and the parallelogram stands on the base$28cm$, find the height of the parallelogram.

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Solution

## Step 1: Find the area of the triangle.Using Heron’s formula, the area of the triangle$=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$So, the perimeter $=26+28+30=84cm$.And it's semi-perimeter$=s=84/2cm=42cm$.$=\surd \left[42\left(42-26\right)\left(42-28\right)\left(42-30\right)\right]c{m}^{2}\phantom{\rule{0ex}{0ex}}=\surd \left[42×16×14×12\right]c{m}^{2}\phantom{\rule{0ex}{0ex}}=336c{m}^{2}$Step 2: calculate the height of the parallelogram.Let the height of the parallelogram be$h$.$Astheareaofparalle\mathrm{log}ram=areaofthetriangle,$$28cm×h=336c{m}^{2}\phantom{\rule{0ex}{0ex}}h=\frac{336}{28}=12cm$Hence, the height of the parallelogram is$12cm.$

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