Question

The area of the triangle below is 9/32 square centimetres. .What is the length of the base? Express your answer as a fraction in simplest form.

Answer 1

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Answer 2

S O L U T I O N :

From the provided figure and given information,

• Area or triangle =
  `\sf (9)/(32)\; cm^2`

• Height of the triangle =
  `\sf (3)/(4)\; cm`

We are asked to calculate the length of base.

As it we know that,

`\\ \twoheadrightarrow\quad \bf{Area_((\Delta)) = (1)/(2) * b * h}\\`

• h denotes height
• b denotes base

So,

`\\ \twoheadrightarrow\quad \sf{(9)/(32)\; cm^2 = (1)/(2) * b * (3)/(4)\; cm}\\`

`\\ \twoheadrightarrow\quad \sf{(9)/(32)\; cm^2 = b * (3)/(8)\; cm}\\`

`\\ \twoheadrightarrow\quad \sf{(9)/(32)\; cm^2/ (3)/(8)\; cm= b }\\`

`\\ \twoheadrightarrow\quad \sf{\frac{\cancel{9} }{\cancel{32} }* \frac{\cancel{8} }{\cancel{3}} \; cm= b }\\`

`\\ \twoheadrightarrow\quad \bf \underline{ (3)/(4)\; cm= b }\\`

Therefore, length of the base of the triangle is 3/4 cm.