Question

2. The base and the height of a triangle are in the ratio 3:7. If the area of
the triangle is 42 cm², find its base and height.​

Answer 1

Given :

• Ratio of Base and height = 3:7 .
• Area of triangle = 42 cm² .

To find:

• Base = ?
• Height = ?

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$\huge\mathfrak{\color{red}{\underline{\underline{༒Answer༒}}}}$

→ Let the base of the triangle be 3x and the height of the triangle be 7x.

→ Area of triangle = 42 cm².

→ But, Area of triangle =

$\frac{1}{2} \times base \times height$

So, we applied this Formula →

→ Area of triangle = 42cm²

→

$\frac{1}{2} \times base \: \times height \: = 42 {cm}^{2}$

→

$\frac{1}{2} \times 3x \times 7x = 42$

→

$\frac{21 {x}^{2} }{2} = 42$

$21 {x}^{2} = 42 \times 2$

→

${x}^{2} = \frac{42 \times 2}{21}$

→

${x}^{2} = 4$

→

$x = \sqrt{4}$

→

$x = 2.$

• Base = 3×2 = $\red{\boxed{\bold{\large{6cm}}}}$
• Height = 7×2 = $\red{\boxed{\bold{\large{14cm}}}}$

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