![\[2:3:4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-06d935806d8b6110d00e554056290099_l3.png "Rendered by QuickLaTeX.com")
(i) It is given that
Perimeter of triangle =
![\[30\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-42f01f219fd66a7db9f04955aaa03f94_l3.png "Rendered by QuickLaTeX.com")
cm
Ratio among sides =
![\[7:5:3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2891677b6747420558bef15e99ba669f_l3.png "Rendered by QuickLaTeX.com")
Here the sum of ratios =
![\[7\text{ }+\text{ }5\text{ }+\text{ }3\text{ }=\text{ }15\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d6250fed1eb392b9393d58ceb96974e6_l3.png "Rendered by QuickLaTeX.com")
We know that
Length of first side =
![\[30\text{ }\times \text{ }7/15\text{ }=\text{ }14\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c235e762f4f67b9f4f5e79b1653304ef_l3.png "Rendered by QuickLaTeX.com")
cm
Length of second side =
![\[30\text{ }\times \text{ }5/15\text{ }=\text{ }10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0d02e1d97efef81bfe42d2fc73b87552_l3.png "Rendered by QuickLaTeX.com")
cm
Length of third side =
![\[~30\text{ }\times \text{ }3/15\text{ }=\text{ }6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2b9f14f758189a2dd966d7766bcd6857_l3.png "Rendered by QuickLaTeX.com")
cm
Therefore, the sides are
![\[14\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-30e216683ad8ac7a76f0fd9b1da36c1e_l3.png "Rendered by QuickLaTeX.com")
cm,
![\[10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e13914576c8f07fa7780b4b1aae684d_l3.png "Rendered by QuickLaTeX.com")
cm and
![\[6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dba464f544e5646eaa291e02993dca75_l3.png "Rendered by QuickLaTeX.com")
cm.
(ii) We know that
Sum of all the angles of a triangle =
![\[{{180}^{0}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-859c9caf7b453840c9ea3fcdb283d6bb_l3.png "Rendered by QuickLaTeX.com")
Here the ratio among angles =
![\[~2:\text{ }3:\text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3cbda82274d645c1237b9152d7cbf053_l3.png "Rendered by QuickLaTeX.com")
Sum of ratios =
![\[2\text{ }+\text{ }3\text{ }+\text{ }4\text{ }=\text{ }9\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dc28d9ac3aa6a967b926002d490758c7_l3.png "Rendered by QuickLaTeX.com")
So we get
First angle =
![\[180\text{ }\times \text{ }2/9\text{ }=\text{ }{{40}^{0}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2c94cfc0adbd6a1e00a2d8bb603a14f7_l3.png "Rendered by QuickLaTeX.com")
Second angle =
![\[180\text{ }\times \text{ }3/9\text{ }=\text{ }{{60}^{0}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3490828626913e40ed989e9e9d513aac_l3.png "Rendered by QuickLaTeX.com")
Third angle =
![\[180\text{ }\times \text{ }4/9\text{ }=\text{ }{{80}^{0}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d0170b6185656a9b304addb2be9bf365_l3.png "Rendered by QuickLaTeX.com")
Hence, the angles are
![\[{{40}^{0}},\text{ }{{60}^{0}}~and\text{ }{{80}^{0}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6c8c217bc50247c72f49fb23097e56cc_l3.png "Rendered by QuickLaTeX.com")
