(i) The sides of a triangle are in the ratio \[7:5:3\] and its perimeter is \[30\] cm. Find the lengths of sides. (ii) If the angles of a triangle are in the ratio \[2:3:4\], find the angles. - Noon Academy

(i) The sides of a triangle are in the ratio

$7:5:3$

and its perimeter is

$30$

cm. Find the lengths of sides. (ii) If the angles of a triangle are in the ratio

$2:3:4$

, find the angles.

Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion

(i) The sides of a triangle are in the ratio

$7:5:3$

and its perimeter is

$30$

cm. Find the lengths of sides. (ii) If the angles of a triangle are in the ratio

$2:3:4$

, find the angles.

(i) It is given that

Perimeter of triangle =

$30$

cm

Ratio among sides =

$7:5:3$

Here the sum of ratios =

$7\text{ }+\text{ }5\text{ }+\text{ }3\text{ }=\text{ }15$

We know that

Length of first side =

$30\text{ }\times \text{ }7/15\text{ }=\text{ }14$

cm

Length of second side =

$30\text{ }\times \text{ }5/15\text{ }=\text{ }10$

cm

Length of third side =

$~30\text{ }\times \text{ }3/15\text{ }=\text{ }6$

cm

Therefore, the sides are

$14$

cm,

$10$

cm and

$6$

cm.

(ii) We know that

Sum of all the angles of a triangle =

${{180}^{0}}$

Here the ratio among angles =

$~2:\text{ }3:\text{ }4$

Sum of ratios =

$2\text{ }+\text{ }3\text{ }+\text{ }4\text{ }=\text{ }9$

So we get

First angle =

$180\text{ }\times \text{ }2/9\text{ }=\text{ }{{40}^{0}}$

Second angle =

$180\text{ }\times \text{ }3/9\text{ }=\text{ }{{60}^{0}}$

Third angle =

$180\text{ }\times \text{ }4/9\text{ }=\text{ }{{80}^{0}}$

Hence, the angles are

${{40}^{0}},\text{ }{{60}^{0}}~and\text{ }{{80}^{0}}$

i

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