List of top Mathematics Questions on Triangles asked in Bihar Board X

An isosceles triangle has \( AB = AC = 13 \) cm. If the length of the perpendicular from vertex \( A \) to \( BC \) is 5 cm, find the length of \( BC \).
Each side of an equilateral triangle \( ABC \) is \( a \). Prove that the altitude of the triangle is \( \frac{\sqrt{3}}{2} a \).
PQRS is a rectangle whose vertices are \( P(0,0) \), \( Q(6,0) \), \( R(6,2) \) and \( S(0,2) \). The area of the rectangle is:
If \( A(a,0) \), \( B(0,0) \), and \( C(0,b) \) are the vertices of \( \triangle ABC \), then the area of \( \triangle ABC \) is:
If an equilateral triangle \( \triangle ABC \) has one side of 12 cm, and another equilateral triangle \( \triangle DEF \) has one side of 6 cm, then what is the ratio of their areas?
In \( \triangle ABC \) and \( \triangle PQR \), which are similar triangles, \( AD \) is perpendicular to \( BC \) and \( PT \) is perpendicular to \( QR \). If \( AD = 9 \) cm and \( PT = 7 \) cm, then the ratio of the areas of triangles \( ABC \) and \( PQR \) is:
If one side of an equilateral triangle is 12 cm, then its height is:
If in \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \) and \( AB = 10 \) cm, \( AC = 14 \) cm, \( BC = 6 \) cm, then the value of \( DC \) is:
In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \). If \( AC = 5.6 \) cm, then \( AE \) is:
If the ratio of corresponding sides of two similar triangles is \( 5:6 \), then the ratio of their perimeters is:
In \( \triangle ABC \), \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm, and \( BC = 6 \) cm, then \( \angle B \) is:
The area of an equilateral triangle is \(36\sqrt{3}\ \text{cm}^2\). Its side is:
In \(\triangle ABC\), points \(X\) on \(AB\) and \(Y\) on \(AC\) satisfy \(XY\parallel BC\). If \(AX:XB=2:3\), then \(AY:YC=\) ?
The ratio of the areas of two similar triangles is \(121:64\). The ratio of their corresponding medians is:
Two similar triangles have perimeters \(30\) cm and \(20\) cm. If a side of the first triangle is \(18\) cm, the corresponding side of the second is: