(D) In $\Delta PQR$,$\angle Q = 90^{\circ}$.Therefore,$\overline{PR}$ is the hypotenuse.By Pythagoras theorem,$PR^2 = PQ^2 + QR^2$.$PR^2 = 8^2 + 15^2

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(D) In $\Delta PQR$,$\angle Q = 90^{\circ}$.Therefore,$\overline{PR}$ is the hypotenuse.By Pythagoras theorem,$PR^2 = PQ^2 + QR^2$.$PR^2 = 8^2 + 15^2 = 64 + 225 = 289$.$PR = \sqrt{289} = 17$.The radius $(r)$ of the incircle of a right-angled triangle is given by the formula $r = \frac{PQ + QR - PR}{2}$.$r = \frac{8 + 15 - 17}{2} = \frac{23 - 17}{2} = \frac{6}{2} = 3$.

Class 10 Mathematics Triangles Mix Examples - Triangles

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In $\Delta PQR$,$\angle Q$ is a right angle. If $PQ = 8$ and $QR = 15$,then the radius of a circle touching all the three sides of $\Delta PQR$ is $\ldots \ldots.$

A
$7$
B
$10$
C
$17$
D
$3$

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Mix Examples - Triangles

In $\Delta XYZ$,$\overline{XM}$ is a median. If $XY = 20$,$XZ = 21$ and $XM = 14.5$,find $YZ$.

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In $\Delta XYZ$,$m\angle X = 90^{\circ}$,$XY = 8$ and $YZ = 17$. Then,the area of $\Delta XYZ$ is.............

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In $\Delta ABC$,$m \angle B = 90^\circ$. If $AC - AB = 27$ and $AC - BC = 6$,find the perimeter of $\Delta ABC$.

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In $\Delta ABC$,$m\angle B = 90^\circ$ and $\overline{BM}$ is an altitude. If $AB = 8$ and $BC = 6$,find $AM$,$BM$,and $CM$.

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The perimeter of square $ABCD$ is $48$. Find the length of its diagonal $\overline{AC}$. (in $\sqrt{2}$)

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In $\Delta PQR$,$\angle Q$ is a right angle. If $PQ = 8$ and $QR = 15$,then the radius of a circle touching all the three sides of $\Delta PQR$ is $\ldots \ldots.$

Similar Questions

In $\Delta XYZ$,$\overline{XM}$ is a median. If $XY = 20$,$XZ = 21$ and $XM = 14.5$,find $YZ$.

In $\Delta XYZ$,$m\angle X = 90^{\circ}$,$XY = 8$ and $YZ = 17$. Then,the area of $\Delta XYZ$ is.............

In $\Delta ABC$,$m \angle B = 90^\circ$. If $AC - AB = 27$ and $AC - BC = 6$,find the perimeter of $\Delta ABC$.

In $\Delta ABC$,$m\angle B = 90^\circ$ and $\overline{BM}$ is an altitude. If $AB = 8$ and $BC = 6$,find $AM$,$BM$,and $CM$.

The perimeter of square $ABCD$ is $48$. Find the length of its diagonal $\overline{AC}$. (in $\sqrt{2}$)

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