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Mathematics

Grade6

Easy

Question

15 cm height triangular board has an area $fraction numerator 345 over denominator 2 end fraction text c end text text m end text to the power of 2 end exponent$ . Find the length of its base.

13 cm
12 cm
$\frac{23}{2}$ cm
$\frac{21}{2}$ cm

hint Hint:

Using the formula area of triangle = $1 half cross times b cross times h$ ,Area and height of triangle is given find the length of base.

The correct answer is: $fraction numerator 23 over denominator 2 end fraction$ cm

Area of a triangular board $equals fraction numerator 345 over denominator 2 end fraction text c end text text m end text to the power of 2 end exponent open parentheses fraction numerator 1 over denominator 2 end fraction h b close parentheses$
Height of the triangular board = 15cm
Using the formula area of triangle = $1 half cross times b cross times h$
The base of the triangle = $2 cross times fraction numerator text area of triangle end text over denominator text height end text end fraction$
$equals 2 cross times 345 over 2 divided by 15$
$equals 345 cross times 1 over 15 open parentheses text reciprocal of 15 is end text fraction numerator 1 over denominator text 15 end text end fraction close parentheses$
$equals 23 space$ cm
Therefore, Length of base of triangle is 23 cm.

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