Question

If the area of a right triangle is 70 cm² and one of the sides containing the right angle is 14 cm. Find the length of other leg.​

Answer 1

Given :

• Area of triangle = 70 cm²
• Length of 1st side = 14 cm

To Find :

• Length of 2nd side = ?

Solution :

Let, another side = x

We know that,

$\underline{\boxed{\bf{ Area \: of \: triangle = \dfrac{1}{2} \times base \times height }}}$

$\underline{\boxed{\bf{ Area \: of \: triangle = \dfrac{1}{2} \times b \times h}}}$

We have :

• Base = x
• Height = 14 cm
• Area of triangle = 70 cm²

On substituting the values :

$\sf : \implies 70 \: cm^{2} = \sf\dfrac{1}{2} \times 14 \: cm \times x$

$\sf : \implies 70 \: cm^{2} = \sf\dfrac{1}{\cancel{2}} \times \cancel{14}_{7} \: cm \times x$

$\sf : \implies 70 \: cm^{2} = 7 \: cm \times x$

$\sf : \implies \dfrac{\cancel{70}^{10} \: cm^{2}}{\cancel{7} \: cm} = x$

$\sf : \implies 10 \: cm = x$

$\underline{\boxed{\bf{x = 10 \: cm}}}$

Hence, Length of 2nd side of triangle is 10 cm.