Concept Checkers – Triangles – Class X

In \(\bigtriangleup ABC,\ DE\| BC\) and \(\frac{AD}{DB}=\frac{3}{5}.\) what is the length of \(AE\) if \(AC=4.8\ cm\) ?

In \(\bigtriangleup ABC\), if \(\frac{AD}{DB}=\frac{AE}{EC}\) and \(\angle ADE=\angle ACB\). What type of triangle is \(\bigtriangleup ABC\) ?

\(X\) and \(Y\) are points on the sides of \(AB\) and \(AC\) respectively of \(\bigtriangleup ABC\) if \(AB=5.6\ cm,\ AX=1.4\ cm,\ AC=7.2\ cm\) and \(XY\| BC\). What is the measure of \(AY\) ?

Given \(\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{4},\) and \(AB=8\ cm\), find \(DC\) ?

A girl of height \(90\ cm\) is walking away from the base of a lamp post at a speed of \(1.2\ m/sec\). If the lamp is \(3.6\ m\) above the ground, find the length of the girl’s shadow after \(4\) seconds.

If \(\bigtriangleup ABC\backsim \bigtriangleup DEF,\ BC=3\ cm,\ EF=4\ cm\) and area of \(\bigtriangleup ABC=54\ cm^{2}\). Find the square of \(\bigtriangleup DEF\).

In \(\bigtriangleup ABC,\ \angle A=90^{\circ},\ AN\perp BC,\ BC=12\ cm\), and \(AC=5\ cm\). Find the ratio \(ar(\bigtriangleup ANC):ar(\bigtriangleup ABC)\) .

In trapezium \(ABCD,\ AB\| CD\). If \(OA=x-4,\ OB=3x-19,\ OC=4\) and \(OD=x-3,\) find ‘\(x\)’ ?

In the given figure, if \(\bigtriangleup ABE\cong\bigtriangleup ACD\), identify the correct statement

The diagonals of a rhombus are \(35\ cm\) and \(12\ cm\). Find the perimeter of the rhombus.

If \(\bigtriangleup ABC\) is an equilateral triangle of side ‘\(a\)’ and \(D\) is a point on BC such that \(BD=\frac{1}{3}BC\), what is the length of \(AD\) ?

If \(\bigtriangleup ABC\backsim\bigtriangleup DEF,\ \angle A=30^{\circ},\ \angle C=50^{\circ},\ AB=5\ cm,\ AC=8\ cm\) and \(DF=7.5\ cm\). Which of the following is true ?

The perimeters of two similar triangles \(ABC\) and \(DEF\) are \(24\ cm\) and \(32\ cm\) respectively. If \(DE=12\ cm\), find \(AB\).

The altitude of two similar triangles are \(4\ cm\) and \(6\ cm\). If the area of one triangle is \(36\ cm^2\), what is the area of the other ?

The ratio of areas of two similar triangle is \(81:49\). If the median of two one triangle is \(4.9\ cm\). What is the median of the other ?

In similar triangle \(\bigtriangleup ABC\) and \(\bigtriangleup FDE, \ DE=4\ cm, BC=\ 8\ cm\) and area of \(\bigtriangleup FDE=25\ cm^2\). What is the area of \(\bigtriangleup ABC\) ?

Given that \(PB\perp AB\) and \(QA\perp AB,\ PO=4\ cm\) and \(QO=7\ cm\), if the area of \(\bigtriangleup QAO\) is \(245\ cm^{2}\), what is the area of \(\bigtriangleup PBO\) ?

In \(\bigtriangleup ABC,\ D\) is a point on \(AB\) and \(E\) is point on \(BC\) such that \(DE\| AC\) and the area of \(\bigtriangleup DBE=\frac{1}{2}\) the area of \(\bigtriangleup ABC\). Find \(\frac{AD}{AB}\).

\(\bigtriangleup ABC\) is an isosceles triangle right angled at \(B\), similar triangles \(ACD\) and \(ABE\) are constructed on sides \(AC\) and \(AB\). Find the ratio between the areas of \(\bigtriangleup ABE\) and \(\bigtriangleup ACD\).

A paper is cut in the following shape, Which of the following is the correct statement ?