If \(\triangle ABC\sim \triangle PQR\), AB = 6.5 cm, PQ = 10.4 cm and perimeter of \(\triangle ABC\) = 60 cm, find the perimeter of \(\triangle PQR\).

3

(a)

It is given that \(\triangle ABC\sim \triangle EDF\) such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.

3

(a)

Find the value of the height 'h' in the adjoining figure. at which the tennis ball must be hit, so that it will just pass over the net and land 6 m away from the base of the net.

3

(a)

In the given figure of \(\triangle ABC\), \(DE\parallel AC\). If \(DC\parallel AP\), where point P lies on BC produced, then prove that \(\frac { BE }{ EC } =\frac { BC }{ CP } \).

3

(a)

ABCD is a trapezium with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Show that \(\frac{AE}{ED}=\frac{BF}{FC}\).

3

(a)

In \(\triangle PQR,ST\parallel QR,\frac { PS }{ SQ } =\frac { 3 }{ 5 } \) and PR = 28 cm, find PT.

3

(a)

In \(\triangle ABC\) , D and E are points on the sides AB and AC respectively, such that \(DE\parallel BC\) . If AD = 4x - 3, AE = 8x - 7, BD = 3x - 1 and CE = 5x - 3, find the value of x.

3

(a)

In the given figure, \(\triangle ABC\) and \(\triangle DBC\) have same base BC and lie on the same side of BC. If \(PQ\parallel BA\) and \(PR\parallel BD\), then prove that \(QR\parallel AD\) .

3

(a)

Find the value of each of the pronumerals in the given pair of triangles. Give reason for your answer.

3

(a)

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

3

(a)

If \(\triangle ABC\sim \triangle QRP\), \(\frac { ar\left( \triangle ABC \right) }{ ar\left( \triangle QRP \right) } =\frac { 9 }{ 4 } \), AB = 18 cm and BC = 15 cm, then find PR.

3

(a)

In the given figure, if  \(DE\parallel BC\), find the ratio of ar \(\left( \triangle ADE \right) \) and ar \(\left( \triangle DECB \right) \)

3

(a)

In \(\triangle PQR,PS\bot QR\) and PS² = QS x RS. Prove that \(\triangle PQR\) is a right angled triangle.

3

(a)

In the given figure, \(\triangle PQR\) is a right angled triangle in which \(\angle Q\) = 90°. If QS = SR, show that PR² = 4 PS² - 3PQ².

3

(a)

In the figure, \(\triangle ABC\) is drawn such that \(AD\bot BC\), then show that AC ² = AB² + BC² - 2BC.BD.

3

(a)