(B) Given that $\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$.Since the triangles are similar,the ratios of their corre

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(B) Given that $\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$.Since the triangles are similar,the ratios of their corresponding sides are equal.Therefore,$\frac{AB}{XY} = \frac{AC}{XZ}$.Substituting the given values: $\frac{4}{5} = \frac{6}{XZ}$.By cross-multiplying,we get $4 \times XZ = 5 \times 6$.$4 \times XZ = 30$.$XZ = \frac{30}{4} = 7.5$.

Class 10 Mathematics Triangles Criteria for Similarity of Triangles

Medium

$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB : XY = 4 : 5$ and $AC = 6$,then $XZ = \ldots$

A
$7$
B
$7.5$
C
$8$
D
$9$

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Class 10

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Triangles

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Criteria for Similarity of Triangles

In $\Delta PQR$,$\angle P$ is a right angle and $\overline{PX}$ is an altitude. If $QX = 4$ and $RX = 5$,then $PQ = \ldots \ldots$

Easy

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In the figure,two chords $AB$ and $CD$ intersect each other at the point $P$. Prove that $AP \cdot PB = CP \cdot DP$.

Medium

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In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle R$. If $AB = 8$,$PQ = 7.5$ and $AC = 6$,find $PR$.

Medium

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In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $YM = 12$ and $XM = 8$,find $XZ$.

Medium

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The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

Medium

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$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB : XY = 4 : 5$ and $AC = 6$,then $XZ = \ldots$

Similar Questions

In $\Delta PQR$,$\angle P$ is a right angle and $\overline{PX}$ is an altitude. If $QX = 4$ and $RX = 5$,then $PQ = \ldots \ldots$

In the figure,two chords $AB$ and $CD$ intersect each other at the point $P$. Prove that $AP \cdot PB = CP \cdot DP$.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle R$. If $AB = 8$,$PQ = 7.5$ and $AC = 6$,find $PR$.

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $YM = 12$ and $XM = 8$,find $XZ$.

The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

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